effective web graph representations
play

Effective Web Graph Representations Giulio Ermanno Pibiri - PowerPoint PPT Presentation

Jul 11, 2023 •279 likes •1.33k views

Effective Web Graph Representations Giulio Ermanno Pibiri University of Pisa and ISTI-CNR Pisa, Italy giulio.pibiri@di.unipi.it Pisa, 29/10/2018 1 Context - Web Graphs Web graphs are directed graphs of pages pointing to other pages on the

  1. k 2 -trees k 2 -ary tree k 2 -trees for Compact Web Graph Representation , representation of the Brisaboa-Ladra-Navarro, SPIRE 2009 adjacency matrix. k = 2 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 00 0111 0100 01 00 10 11 Credits to A. Gómez-Brandón

  2. k 2 -trees k 2 -ary tree k 2 -trees for Compact Web Graph Representation , representation of the Brisaboa-Ladra-Navarro, SPIRE 2009 adjacency matrix. k = 2 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 00 0111 0100 01 00 10 01 00 11 Credits to A. Gómez-Brandón

  3. k 2 -trees k 2 -ary tree k 2 -trees for Compact Web Graph Representation , representation of the Brisaboa-Ladra-Navarro, SPIRE 2009 adjacency matrix. k = 2 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 00 0111 0100 01 00 10 01 00 1110101010001001 00011101000100100100 T L 11 Credits to A. Gómez-Brandón

  4. k 2 -trees k 2 -ary tree k 2 -trees for Compact Web Graph Representation , representation of the Brisaboa-Ladra-Navarro, SPIRE 2009 adjacency matrix. k = 2 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 00 0111 0100 01 00 10 01 00 Access 1110101010001001 00011101000100100100 T L 11 Credits to A. Gómez-Brandón

  5. k 2 -trees k 2 -ary tree k 2 -trees for Compact Web Graph Representation , representation of the Brisaboa-Ladra-Navarro, SPIRE 2009 adjacency matrix. k = 2 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 00 0111 0100 01 00 10 01 00 Access 1110101010001001 00011101000100100100 1 T L 11 Credits to A. Gómez-Brandón

  6. k 2 -trees k 2 -ary tree k 2 -trees for Compact Web Graph Representation , representation of the Brisaboa-Ladra-Navarro, SPIRE 2009 adjacency matrix. k = 2 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 00 0111 0100 01 00 10 01 00 Access 1110101010001001 00011101000100100100 1 0 T L 11 Credits to A. Gómez-Brandón

  7. k 2 -trees k 2 -ary tree k 2 -trees for Compact Web Graph Representation , representation of the Brisaboa-Ladra-Navarro, SPIRE 2009 adjacency matrix. k = 2 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 00 0111 0100 01 00 10 01 00 Access 1110101010001001 00011101000100100100 1 0 1 T L 11 Credits to A. Gómez-Brandón

  8. k 2 -trees k 2 -ary tree k 2 -trees for Compact Web Graph Representation , representation of the Brisaboa-Ladra-Navarro, SPIRE 2009 adjacency matrix. k = 2 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 00 0111 0100 01 00 10 01 00 Access 1110101010001001 00011101000100100100 1 0 1 1 0 T L 11 Credits to A. Gómez-Brandón

  9. k 2 -trees k 2 -ary tree k 2 -trees for Compact Web Graph Representation , representation of the Brisaboa-Ladra-Navarro, SPIRE 2009 adjacency matrix. k = 2 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 00 0111 0100 01 00 10 1 01 00 Access 1110101010001001 00011101000100100100 1 0 1 1 0 1 T L 11 Credits to A. Gómez-Brandón

  10. k 2 -trees k 2 -ary tree k 2 -trees for Compact Web Graph Representation , representation of the Brisaboa-Ladra-Navarro, SPIRE 2009 adjacency matrix. k = 2 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 00 0111 0100 01 00 10 1 01 00 Access 1110101010001001 00011101000100100100 1 0 1 1 0 1 T L rank 1 x k 2 on T in O(1) 11 Credits to A. Gómez-Brandón

  11. <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">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</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">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</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">ACa3icbVHbSsNAEN3Ge7219k19CFbBylJEfSlIPrio7faQg2y2U7q0s0m7k6qNfQTfNVv8yP8BzexiK0OLBzOnJk9M+PHgmt0nI+CNTM7N7+wuFRcXldWy+VN251lCgGTRaJSLV9qkFwCU3kKAdK6ChL6Dl98+yfGsASvNI3uAwBi+kPckDziga6no3L0vVZ2ak4f9F7hjUCXjuLgvF67uhFLQpDIBNW64zoxeilVyJmAUfEu0RBT1qc96BgoaQjaS3OvI3vPMF07iJR5Eu2c/V2R0lDrYegbZUjxQU/nMvK/XCfB4NhLuYwTBMm+PwoSYWNkZ4PbXa6AoRgaQJnixqvNHqiDM16JjohNgIqNBzkhW4DVQJeKrgPZkI5NeCAqsfES1/4ST/I/dSCU/4nPueUNy4XprtIHNbNFdwp3f+F9zWa65Tcy/r1ZPT8T0WyRbZIfvEJUfkhJyTC9IkjPTIK3kj74VPq2JtWtvfUqswrqmQibD2vgA9J72S</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> k 2 -trees pages links m n h = d log k 2 n 2 e 12

  12. <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">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</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">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</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">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</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">ACa3icbVHbSsNAEN3Ge7219k19CFbBylJEfSlIPrio7faQg2y2U7q0s0m7k6qNfQTfNVv8yP8BzexiK0OLBzOnJk9M+PHgmt0nI+CNTM7N7+wuFRcXldWy+VN251lCgGTRaJSLV9qkFwCU3kKAdK6ChL6Dl98+yfGsASvNI3uAwBi+kPckDziga6npX7t6Xqk7NycP+C9wxqJxXNyXC1d3YglIUhkgmrdcZ0YvZQq5EzAqHiXaIgp69MedAyUNATtpbnXkb1nmK4dRMo8iXbO/q5Iaj1MPSNMqT4oKdzGflfrpNgcOylXMYJgmTfHwWJsDGys8HtLlfAUAwNoEx49VmD1RhmY9E50QGwEVGg7yQreBKgEvFdwHM6GcGnBA1WPipS/8cJL/kXuphCd8zn1PKG5cL812kLktmiu40zv/C27rNdepuZf16snp+B6LZIvskH3ikiNyQs7JBWkSRnrklbyR98KnVbE2re1vqVUY1TIRFh7Xz8tvZM=</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="ZcH8CFXU8ogNkvQgJVXU7TE92p8=">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</latexit> <latexit sha1_base64="ZcH8CFXU8ogNkvQgJVXU7TE92p8=">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</latexit> <latexit sha1_base64="ZcH8CFXU8ogNkvQgJVXU7TE92p8=">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</latexit> <latexit sha1_base64="ZcH8CFXU8ogNkvQgJVXU7TE92p8=">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</latexit> k 2 -trees pages links m n h = d log k 2 n 2 e mk 2 d log k 2 n 2 e So the total space is bits 12

  13. <latexit sha1_base64="zquE5A6lB8UBOe/kQIeymHphjGU=">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</latexit> <latexit sha1_base64="zquE5A6lB8UBOe/kQIeymHphjGU=">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</latexit> <latexit sha1_base64="zquE5A6lB8UBOe/kQIeymHphjGU=">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</latexit> <latexit sha1_base64="zquE5A6lB8UBOe/kQIeymHphjGU=">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</latexit> <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">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</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">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</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">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</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="baC/QgKlqxwLkJFIqQiUzIlvLpg=">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</latexit> <latexit sha1_base64="baC/QgKlqxwLkJFIqQiUzIlvLpg=">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</latexit> <latexit sha1_base64="baC/QgKlqxwLkJFIqQiUzIlvLpg=">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</latexit> <latexit sha1_base64="baC/QgKlqxwLkJFIqQiUzIlvLpg=">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</latexit> <latexit sha1_base64="ZcH8CFXU8ogNkvQgJVXU7TE92p8=">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</latexit> <latexit sha1_base64="ZcH8CFXU8ogNkvQgJVXU7TE92p8=">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</latexit> <latexit sha1_base64="ZcH8CFXU8ogNkvQgJVXU7TE92p8=">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</latexit> <latexit sha1_base64="ZcH8CFXU8ogNkvQgJVXU7TE92p8=">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</latexit> <latexit sha1_base64="IaMT6pNFtZSw6pMZqG5LsTnJFM=">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</latexit> <latexit sha1_base64="IaMT6pNFtZSw6pMZqG5LsTnJFM=">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</latexit> <latexit sha1_base64="IaMT6pNFtZSw6pMZqG5LsTnJFM=">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</latexit> <latexit sha1_base64="IaMT6pNFtZSw6pMZqG5LsTnJFM=">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</latexit> k 2 -trees pages links m n h = d log k 2 n 2 e mk 2 d log k 2 n 2 e So the total space is bits k 2 Õ b log k 2 m c� 1 k 2 i + mk 2 ( d log k 2 n e � b log k 2 m c ) i = 0 k 2 − 1 + mk 2 log k 2 n 2 = k 2 m − 1 m = mk 2 ⇣ ⌘ log k 2 n 2 m + O ( 1 ) bits 12

  14. <latexit sha1_base64="IaMT6pNFtZSw6pMZqG5LsTnJFM=">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</latexit> <latexit sha1_base64="IaMT6pNFtZSw6pMZqG5LsTnJFM=">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</latexit> <latexit sha1_base64="IaMT6pNFtZSw6pMZqG5LsTnJFM=">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</latexit> <latexit sha1_base64="IaMT6pNFtZSw6pMZqG5LsTnJFM=">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</latexit> <latexit sha1_base64="qtM+GcnR9beauqclPCs41pO2F1k=">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</latexit> <latexit sha1_base64="qtM+GcnR9beauqclPCs41pO2F1k=">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</latexit> <latexit sha1_base64="qtM+GcnR9beauqclPCs41pO2F1k=">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</latexit> <latexit sha1_base64="qtM+GcnR9beauqclPCs41pO2F1k=">ACpHicbVFdaxNBFJ1s/ajxK7WPvgymSkUJu0GwCIWiLz4IVm3aQnYbZid3k6HzsZ252zYd8l/8Nb7q/G2W0Qk3ph4HDOuTP3nslLKRzG8e9WtHbr9p276/fa9x8fPS4s/Hk0JnKchwI409zpkDKTQMUKCE49ICU7mEo/z0Q60fnYN1wugDnJWQKTbRohCcYaBGnXdbqTQT6vVJn6Z8aowDquY0ZWVpzSVtJHTwjJe+Y+iK/o5231cmvU6ca9uCl6EyQL0CWL2h9tL6mY8MrBRq5ZM4Nk7jEzDOLgkuYt9PKQcn4KZvAMEDNFLjMN0vO6fPAjGlhbDgacP+2+GZcm6m8uBUDKduVavJ/2nDCoudzAtdVgiaXz9UVJKioXVidCwscJSzABi3IsxK+ZSFQDkunQT4m7BpIPXTWOyi7aCzEuRQ9hQryx4zuxZlfkr8WaZ/2vPvIYLvGzmXnIcJmvM6inbYdfSFYzvwkO+70k7iVf+t294v/WCdPyTOyTRLyluyRj2SfDAgn38kP8pP8il5En6Jv0eDaGrUWPZtkqaKTP5gF0gc=</latexit> <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">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</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">ACa3icbVHbSsNAEN3Ge7219k19CFbBylJEfSlIPrio7faQg2y2U7q0s0m7k6qNfQTfNVv8yP8BzexiK0OLBzOnJk9M+PHgmt0nI+CNTM7N7+wuFRcXldWy+VN251lCgGTRaJSLV9qkFwCU3kKAdK6ChL6Dl98+yfGsASvNI3uAwBi+kPckDziga6no3L0vVZ2ak4f9F7hjUCXjuLgvF67uhFLQpDIBNW64zoxeilVyJmAUfEu0RBT1qc96BgoaQjaS3OvI3vPMF07iJR5Eu2c/V2R0lDrYegbZUjxQU/nMvK/XCfB4NhLuYwTBMm+PwoSYWNkZ4PbXa6AoRgaQJnixqvNHqiDM16JjohNgIqNBzkhW4DVQJeKrgPZkI5NeCAqsfES1/4ST/I/dSCU/4nPueUNy4XprtIHNbNFdwp3f+F9zWa65Tcy/r1ZPT8T0WyRbZIfvEJUfkhJyTC9IkjPTIK3kj74VPq2JtWtvfUqswrqmQibD2vgA9J72S</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">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</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="baC/QgKlqxwLkJFIqQiUzIlvLpg=">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</latexit> <latexit sha1_base64="baC/QgKlqxwLkJFIqQiUzIlvLpg=">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</latexit> <latexit sha1_base64="baC/QgKlqxwLkJFIqQiUzIlvLpg=">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</latexit> <latexit sha1_base64="baC/QgKlqxwLkJFIqQiUzIlvLpg=">ACnHicbVFdixMxFE3Hr7V+dfVRkGBX6KUSRH0pbCsPgirLtLnTGknvdEOTzJjcWa2h/8Nf46v+Bf+NmdkituFwMm5yb3npuVSjqM49+t6MrVa9dv7Nxs37p95+69zu79sSsqK2AkClXY04w7UNLACUqOC0tcJ0pOMkWr+r8yTlYJwtzjMsSUs3nRuZScAzUtDPYo0OqF58GNDmU816ivnUh+sqyS0X3gTk9Yo+pe97bL+W7O9NO924HzdBLwO2Bl2yjqPpbutjMitEpcGgUNy5CYtLTD23KIWCVTupHJRcLPgcJgEarsGlvhluRZ8EZkbzwoZjkDbsvxWea+eWOgtKzfHMbedq8n+5SYX5y9RLU1YIRlx8lFeKYkFrp+hMWhColgFwYWXolYozHlzB4OfGS4jDnCsHz5pCNkRbQeqVzCBMaLYGPOf2c5X6b/L5Jv9XnoDX/Br0/eG4pilvag7rYdtsC2Pb8MxoM+i/vsw6B7cLjexw5SB6THmHkBTkgb8gRGRFBvpMf5Cf5FT2KXkdvo3cX0qi1rnlANiIa/wHoKc3e</latexit> <latexit sha1_base64="ZcH8CFXU8ogNkvQgJVXU7TE92p8=">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</latexit> <latexit sha1_base64="ZcH8CFXU8ogNkvQgJVXU7TE92p8=">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</latexit> <latexit sha1_base64="ZcH8CFXU8ogNkvQgJVXU7TE92p8=">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</latexit> <latexit sha1_base64="ZcH8CFXU8ogNkvQgJVXU7TE92p8=">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</latexit> <latexit sha1_base64="zquE5A6lB8UBOe/kQIeymHphjGU=">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</latexit> <latexit sha1_base64="zquE5A6lB8UBOe/kQIeymHphjGU=">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</latexit> <latexit sha1_base64="zquE5A6lB8UBOe/kQIeymHphjGU=">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</latexit> <latexit sha1_base64="zquE5A6lB8UBOe/kQIeymHphjGU=">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</latexit> k 2 -trees pages links m n h = d log k 2 n 2 e mk 2 d log k 2 n 2 e So the total space is bits k 2 Õ b log k 2 m c� 1 k 2 i + mk 2 ( d log k 2 n e � b log k 2 m c ) i = 0 k 2 − 1 + mk 2 log k 2 n 2 = k 2 m − 1 m = mk 2 ⇣ ⌘ log k 2 n 2 m + O ( 1 ) bits Information theoretic lower bound � ≈ m log n 2 log � n 2 m + O ( m ) m 12

  15. <latexit sha1_base64="Tgx5KLqGqdh0VCG2Hx81MtAfG8=">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</latexit> <latexit sha1_base64="Tgx5KLqGqdh0VCG2Hx81MtAfG8=">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</latexit> <latexit sha1_base64="Tgx5KLqGqdh0VCG2Hx81MtAfG8=">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</latexit> <latexit sha1_base64="Tgx5KLqGqdh0VCG2Hx81MtAfG8=">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</latexit> <latexit sha1_base64="qtM+GcnR9beauqclPCs41pO2F1k=">ACpHicbVFdaxNBFJ1s/ajxK7WPvgymSkUJu0GwCIWiLz4IVm3aQnYbZid3k6HzsZ252zYd8l/8Nb7q/G2W0Qk3ph4HDOuTP3nslLKRzG8e9WtHbr9p276/fa9x8fPS4s/Hk0JnKchwI409zpkDKTQMUKCE49ICU7mEo/z0Q60fnYN1wugDnJWQKTbRohCcYaBGnXdbqTQT6vVJn6Z8aowDquY0ZWVpzSVtJHTwjJe+Y+iK/o5231cmvU6ca9uCl6EyQL0CWL2h9tL6mY8MrBRq5ZM4Nk7jEzDOLgkuYt9PKQcn4KZvAMEDNFLjMN0vO6fPAjGlhbDgacP+2+GZcm6m8uBUDKduVavJ/2nDCoudzAtdVgiaXz9UVJKioXVidCwscJSzABi3IsxK+ZSFQDkunQT4m7BpIPXTWOyi7aCzEuRQ9hQryx4zuxZlfkr8WaZ/2vPvIYLvGzmXnIcJmvM6inbYdfSFYzvwkO+70k7iVf+t294v/WCdPyTOyTRLyluyRj2SfDAgn38kP8pP8il5En6Jv0eDaGrUWPZtkqaKTP5gF0gc=</latexit> <latexit sha1_base64="qtM+GcnR9beauqclPCs41pO2F1k=">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</latexit> <latexit sha1_base64="qtM+GcnR9beauqclPCs41pO2F1k=">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</latexit> <latexit sha1_base64="qtM+GcnR9beauqclPCs41pO2F1k=">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</latexit> <latexit sha1_base64="baC/QgKlqxwLkJFIqQiUzIlvLpg=">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</latexit> <latexit sha1_base64="baC/QgKlqxwLkJFIqQiUzIlvLpg=">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</latexit> <latexit sha1_base64="baC/QgKlqxwLkJFIqQiUzIlvLpg=">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</latexit> <latexit sha1_base64="baC/QgKlqxwLkJFIqQiUzIlvLpg=">ACnHicbVFdixMxFE3Hr7V+dfVRkGBX6KUSRH0pbCsPgirLtLnTGknvdEOTzJjcWa2h/8Nf46v+Bf+NmdkituFwMm5yb3npuVSjqM49+t6MrVa9dv7Nxs37p95+69zu79sSsqK2AkClXY04w7UNLACUqOC0tcJ0pOMkWr+r8yTlYJwtzjMsSUs3nRuZScAzUtDPYo0OqF58GNDmU816ivnUh+sqyS0X3gTk9Yo+pe97bL+W7O9NO924HzdBLwO2Bl2yjqPpbutjMitEpcGgUNy5CYtLTD23KIWCVTupHJRcLPgcJgEarsGlvhluRZ8EZkbzwoZjkDbsvxWea+eWOgtKzfHMbedq8n+5SYX5y9RLU1YIRlx8lFeKYkFrp+hMWhColgFwYWXolYozHlzB4OfGS4jDnCsHz5pCNkRbQeqVzCBMaLYGPOf2c5X6b/L5Jv9XnoDX/Br0/eG4pilvag7rYdtsC2Pb8MxoM+i/vsw6B7cLjexw5SB6THmHkBTkgb8gRGRFBvpMf5Cf5FT2KXkdvo3cX0qi1rnlANiIa/wHoKc3e</latexit> <latexit sha1_base64="BQLSO+fKbzOpsVJ6BMutFkKwzjg=">ACbXicbVHbSsNAEN3GW623VvFJkWAVfZCSFEFfCqIvPlaxKtQgm+3ELt1s4u6kWoPf4Kt+ml/hL7hJi9jqwMLhzJnZMzN+LhGx/ksWFPTM7NzxfnSwuLS8kq5snqto0QxaLFIROrWpxoEl9BCjgJuYwU09AXc+L2zLH/TB6V5JK9wEIMX0gfJA84oGq102vUd+7LVafm5GH/Be4IVMkomveVwuVdJ2JCBKZoFq3XSdGL6UKORPwWrpLNMSU9egDtA2UNATtpbnbV3vXMB07iJR5Eu2c/V2R0lDrQegbZUixqydzGflfrp1gcOylXMYJgmTDj4JE2BjZ2eh2hytgKAYGUKa48WqzLlWUoVnQWCfERkCFhoO80G2gSsBLBfBTCgnBuxT9Zh46Qs/HOd/5F4q4Qmfc9jivXS7MdZG5L5gru5M7/gut6zXVq7kW9enI6ukeRbJBtsk9ckROyDlpkhZhJM38k4+Cl/WurVpbQ2lVmFUs0bGwtr7BmXzvhM=</latexit> <latexit sha1_base64="BQLSO+fKbzOpsVJ6BMutFkKwzjg=">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</latexit> <latexit sha1_base64="BQLSO+fKbzOpsVJ6BMutFkKwzjg=">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</latexit> <latexit sha1_base64="BQLSO+fKbzOpsVJ6BMutFkKwzjg=">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</latexit> <latexit sha1_base64="zquE5A6lB8UBOe/kQIeymHphjGU=">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</latexit> <latexit sha1_base64="zquE5A6lB8UBOe/kQIeymHphjGU=">AC5nicfVHLbhMxFPUMrxAeTcqSjUWKVASNZiIk2ESqYMOyoKatlJlEHudOYsWPwfYUgplfYIfY8lts+RI8kwg1KeKujs451z73qzgzNgo+hWEN27eun2ndbd97/6Dh3ud7v6ZUaWmMK32REQOcSRhZjlcFBqIyDicZ8u3tX5+CdowJU/tqoBUkLlkOaPEemra+XqwnAxwYkoxdWwYVROX8JwrpXHC1XzqvFphgRO9Jo9wXOHlxA1YhZ9j4dXDhFNg/KpdenvDHeH/PfbsYNrpRf2oKXwdxBvQ5s6mXaD8lM0VKAtJQTY8ZxVNjUEW0Z5VC1k9JAQeiSzGHsoSQCTOqaNVX4qWdmOPdxciUtbtirHY4IY1Yi805B7MLsajX5L21c2vx16pgsSguSrj/KS46twvXO8YxpoJavPCBUM58V0wXRhFp/ma2XrB3mhBt40TGQ6tLSB1nGfgJ5c6Al0R/LFP3hb3c5v/aUyfhk/3c5N5ynMapq3dQp237K8S7O78Ozgb9OrH7we94zebe7TQY/QEHaIYvULH6B06QSNE0e+gFXSD/XARfgu/hz/W1jDY9DxCWxX+/APcEejK</latexit> <latexit sha1_base64="zquE5A6lB8UBOe/kQIeymHphjGU=">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</latexit> <latexit sha1_base64="zquE5A6lB8UBOe/kQIeymHphjGU=">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</latexit> <latexit sha1_base64="ZcH8CFXU8ogNkvQgJVXU7TE92p8=">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</latexit> <latexit sha1_base64="ZcH8CFXU8ogNkvQgJVXU7TE92p8=">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</latexit> <latexit sha1_base64="ZcH8CFXU8ogNkvQgJVXU7TE92p8=">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</latexit> <latexit sha1_base64="ZcH8CFXU8ogNkvQgJVXU7TE92p8=">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</latexit> <latexit sha1_base64="IaMT6pNFtZSw6pMZqG5LsTnJFM=">ACo3icbVFNbxMxEHWj5bwlcKRi0VaCQmI1hES9BCpgsSl1IlbaVkibzObGrF9m7t2Zg7W/h13CFM/8G7yZCJGUky89v3tgz2mhpM4/t2Kbt2+c3dn917/oOHjx539p6cury0AkYiV7k9T7kDJQ2MUKC8IC16mCs3Txoc6fXYF1MjdDXBaQaD43MpOCY6CmncN9OqCL306ySwXr9mlQ/HsNGXVDcJlc+nNVetJCYgr6v9acb9+Im6E3A1qBL1nE83WudTGa5KDUYFIo7N2ZxgYnFqVQULUnpYOCiwWfwzhAwzW4xDczVvQgMDOa5TYsg7Rh/63wXDu31GlQao4XbjtXk/LjUvM3iVemqJEMGL1UFYqijmtDaMzaUGgWgbAhZWhVyoueHACg60bNyEOMq4cvGoK2QBtCYlXMoUwodka8IrbyzLx3+SbTf6vPEGrvFr0/eGYsgSX3tQd9sOv8C2Pb8JTvs9FvfY53736P36P3bJM/KcvCMvCVH5CM5JiMiyHfyg/wkv6KD6FN0Eg1X0qi1rnlKNiJK/gC8M9FN</latexit> <latexit sha1_base64="IaMT6pNFtZSw6pMZqG5LsTnJFM=">ACo3icbVFNbxMxEHWj5bwlcKRi0VaCQmI1hES9BCpgsSl1IlbaVkibzObGrF9m7t2Zg7W/h13CFM/8G7yZCJGUky89v3tgz2mhpM4/t2Kbt2+c3dn917/oOHjx539p6cury0AkYiV7k9T7kDJQ2MUKC8IC16mCs3Txoc6fXYF1MjdDXBaQaD43MpOCY6CmncN9OqCL306ySwXr9mlQ/HsNGXVDcJlc+nNVetJCYgr6v9acb9+Im6E3A1qBL1nE83WudTGa5KDUYFIo7N2ZxgYnFqVQULUnpYOCiwWfwzhAwzW4xDczVvQgMDOa5TYsg7Rh/63wXDu31GlQao4XbjtXk/LjUvM3iVemqJEMGL1UFYqijmtDaMzaUGgWgbAhZWhVyoueHACg60bNyEOMq4cvGoK2QBtCYlXMoUwodka8IrbyzLx3+SbTf6vPEGrvFr0/eGYsgSX3tQd9sOv8C2Pb8JTvs9FvfY53736P36P3bJM/KcvCMvCVH5CM5JiMiyHfyg/wkv6KD6FN0Eg1X0qi1rnlKNiJK/gC8M9FN</latexit> <latexit sha1_base64="IaMT6pNFtZSw6pMZqG5LsTnJFM=">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</latexit> <latexit sha1_base64="IaMT6pNFtZSw6pMZqG5LsTnJFM=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">ACa3icbVHbSsNAEN3Ge7219k19CFbBylJEfSlIPrio7faQg2y2U7q0s0m7k6qNfQTfNVv8yP8BzexiK0OLBzOnJk9M+PHgmt0nI+CNTM7N7+wuFRcXldWy+VN251lCgGTRaJSLV9qkFwCU3kKAdK6ChL6Dl98+yfGsASvNI3uAwBi+kPckDziga6npX7t6Xqk7NycP+C9wxqJxXNyXC1d3YglIUhkgmrdcZ0YvZQq5EzAqHiXaIgp69MedAyUNATtpbnXkb1nmK4dRMo8iXbO/q5Iaj1MPSNMqT4oKdzGflfrpNgcOylXMYJgmTfHwWJsDGys8HtLlfAUAwNoEx49VmD1RhmY9E50QGwEVGg7yQreBKgEvFdwHM6GcGnBA1WPipS/8cJL/kXuphCd8zn1PKG5cL812kLktmiu40zv/C27rNdepuZf16snp+B6LZIvskH3ikiNyQs7JBWkSRnrklbyR98KnVbE2re1vqVUY1TIRFh7Xz8tvZM=</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">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</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">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</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">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</latexit> <latexit sha1_base64="+UqRfLisYEzOB0bIvJMLaODzI=">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</latexit> <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> <latexit sha1_base64="NBm/54KWBqYjwdzq4/XS3LU5RmQ=">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</latexit> k 2 -trees pages links m n h = d log k 2 n 2 e mk 2 d log k 2 n 2 e So the total space is bits k 2 Õ b log k 2 m c� 1 k 2 i + mk 2 ( d log k 2 n e � b log k 2 m c ) i = 0 k 2 − 1 + mk 2 log k 2 n 2 = k 2 m − 1 m = mk 2 ⇣ ⌘ log k 2 n 2 m + O ( 1 ) bits k = 2 Information theoretic 2 m log n 2 m + O ( m ) lower bound � ≈ m log n 2 log � n 2 m + O ( m ) 2X away m 12

  16. k 2 -trees Space results in bits x link. 13

  17. Block-trees A block-tree divides a string into fixed- Queries on LZ-Bounded Encodings , size blocks and those appearing Belazzougui et al., DCC 2014 earlier are represented with pointers. 14 Credits to A. Gómez-Brandón

  18. Block-trees A block-tree divides a string into fixed- Queries on LZ-Bounded Encodings , size blocks and those appearing Belazzougui et al., DCC 2014 earlier are represented with pointers. AABAABBAABAACBBA input = 14 Credits to A. Gómez-Brandón

  19. Block-trees A block-tree divides a string into fixed- Queries on LZ-Bounded Encodings , size blocks and those appearing Belazzougui et al., DCC 2014 earlier are represented with pointers. AABAABBAABAACBBA input = AABAABBA ABAACBBA 14 Credits to A. Gómez-Brandón

  20. Block-trees A block-tree divides a string into fixed- Queries on LZ-Bounded Encodings , size blocks and those appearing Belazzougui et al., DCC 2014 earlier are represented with pointers. AABAABBAABAACBBA input = AABAABBA ABAACBBA AABA ABBA 14 Credits to A. Gómez-Brandón

  21. Block-trees A block-tree divides a string into fixed- Queries on LZ-Bounded Encodings , size blocks and those appearing Belazzougui et al., DCC 2014 earlier are represented with pointers. AABAABBAABAACBBA input = AABAABBA ABAACBBA AABA ABBA ABAA CBBA 14 Credits to A. Gómez-Brandón

  22. Block-trees A block-tree divides a string into fixed- Queries on LZ-Bounded Encodings , size blocks and those appearing Belazzougui et al., DCC 2014 earlier are represented with pointers. AABAABBAABAACBBA input = AABAABBA ABAACBBA AABA ABBA ABAA CBBA offset=1 14 Credits to A. Gómez-Brandón

  23. Block-trees A block-tree divides a string into fixed- Queries on LZ-Bounded Encodings , size blocks and those appearing Belazzougui et al., DCC 2014 earlier are represented with pointers. AABAABBAABAACBBA input = AABAABBA ABAACBBA AABA ABBA ABAA CBBA offset=1 AA BA 14 Credits to A. Gómez-Brandón

  24. Block-trees A block-tree divides a string into fixed- Queries on LZ-Bounded Encodings , size blocks and those appearing Belazzougui et al., DCC 2014 earlier are represented with pointers. AABAABBAABAACBBA input = AABAABBA ABAACBBA AABA ABBA ABAA CBBA offset=1 AA BA AB BA 14 Credits to A. Gómez-Brandón

  25. Block-trees A block-tree divides a string into fixed- Queries on LZ-Bounded Encodings , size blocks and those appearing Belazzougui et al., DCC 2014 earlier are represented with pointers. AABAABBAABAACBBA input = AABAABBA ABAACBBA AABA ABBA ABAA CBBA offset=1 AA BA AB BA offset=1 14 Credits to A. Gómez-Brandón

  26. Block-trees A block-tree divides a string into fixed- Queries on LZ-Bounded Encodings , size blocks and those appearing Belazzougui et al., DCC 2014 earlier are represented with pointers. AABAABBAABAACBBA input = AABAABBA ABAACBBA AABA ABBA ABAA CBBA offset=1 AA BA AB BA offset=1 offset=0 14 Credits to A. Gómez-Brandón

  27. Block-trees A block-tree divides a string into fixed- Queries on LZ-Bounded Encodings , size blocks and those appearing Belazzougui et al., DCC 2014 earlier are represented with pointers. AABAABBAABAACBBA input = AABAABBA ABAACBBA AABA ABBA ABAA CBBA offset=1 AA BA AB BA CB BA offset=1 offset=0 14 Credits to A. Gómez-Brandón

  28. Block-trees A block-tree divides a string into fixed- Queries on LZ-Bounded Encodings , size blocks and those appearing Belazzougui et al., DCC 2014 earlier are represented with pointers. AABAABBAABAACBBA input = AABAABBA ABAACBBA AABA ABBA ABAA CBBA offset=1 AA BA AB BA CB BA offset=1 offset=0 offset=0 14 Credits to A. Gómez-Brandón

  29. Block-trees A block-tree divides a string into fixed- Queries on LZ-Bounded Encodings , size blocks and those appearing Belazzougui et al., DCC 2014 earlier are represented with pointers. AABAABBAABAACBBA input = offset=1 AA BA CB offset=0 offset=1 offset=0 15 Credits to A. Gómez-Brandón

  30. Block-trees A block-tree divides a string into fixed- Queries on LZ-Bounded Encodings , size blocks and those appearing Belazzougui et al., DCC 2014 earlier are represented with pointers. AABAABBAABAACBBA input = Access(4) = ? offset=1 AA BA CB offset=0 offset=1 offset=0 15 Credits to A. Gómez-Brandón

  31. Block-trees A block-tree divides a string into fixed- Queries on LZ-Bounded Encodings , size blocks and those appearing Belazzougui et al., DCC 2014 earlier are represented with pointers. AABAABBAABAACBBA input = Access(4) = ? offset=1 AA BA CB offset=0 offset=1 offset=0 15 Credits to A. Gómez-Brandón

  32. Block-trees A block-tree divides a string into fixed- Queries on LZ-Bounded Encodings , size blocks and those appearing Belazzougui et al., DCC 2014 earlier are represented with pointers. AABAABBAABAACBBA input = Access(4) = ? offset=1 AA BA CB offset=0 offset=1 offset=0 15 Credits to A. Gómez-Brandón

  33. Block-trees A block-tree divides a string into fixed- Queries on LZ-Bounded Encodings , size blocks and those appearing Belazzougui et al., DCC 2014 earlier are represented with pointers. AABAABBAABAACBBA input = Access(4) = ? offset=1 AA BA CB offset=0 offset=1 offset=0 15 Credits to A. Gómez-Brandón

  34. Block-trees A block-tree divides a string into fixed- Queries on LZ-Bounded Encodings , size blocks and those appearing Belazzougui et al., DCC 2014 earlier are represented with pointers. AABAABBAABAACBBA A input = A Access(4) = ? offset=1 AA BA CB offset=0 offset=1 offset=0 15 Credits to A. Gómez-Brandón

  35. Block-trees A block-tree divides a string into fixed- Queries on LZ-Bounded Encodings , size blocks and those appearing Belazzougui et al., DCC 2014 earlier are represented with pointers. AABAABBAABAACBBA A input = A Access(4) = ? offset=1 AA BA CB offset=0 offset=1 offset=0 Compression ratios close to Lempel-Ziv in practice and access to any subsequence. 15 Credits to A. Gómez-Brandón

  36. <latexit sha1_base64="VdTUT9ozay0Vmujujxr5ThUjYU=">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</latexit> <latexit sha1_base64="VdTUT9ozay0Vmujujxr5ThUjYU=">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</latexit> <latexit sha1_base64="VdTUT9ozay0Vmujujxr5ThUjYU=">ACcHicbVHBatAEF2pSeO6aeO0l0IOVesUQghGCoX0EgjtJce0xLHBFmG0HtmLVyt1d+TUFfmJXNMf62/0C7pSRInsDiw83ryZfTMTZVIY8v3fjvtkY/PpVutZ+/n2i5c7nd1XVybNc+T2WqhxEYlEJhnwRJHGYaIYkDqL5lzI/WKA2IlWXtMwTGCqRCw4kKWG+2MjpgnsX3e6fs+vwlsHQ26rI6L613n23iS8jxBRVyCMaPAzygsQJPgEm/b49xgBnwOUxZqCBExaV4Vvg2UmXpxq+xR5Ffu4oDEmGUSWUCNDOruZL8X26U/wpLITKckLFHz6Kc+lR6pXTexOhkZNcWgBcC+vV4zPQwMnuqNGJ6DQGafCoKgxOSecYFlJEaCdUKwMuQH/Pw+Kn+Njk/8nDQuEN/ah8NxSXQViUOyjdtu0VgtWdr4Or417g94Kvx92z/U9WmyPvWcHLGAn7IydswvWZ5xJdsfu2S/nj/vGfeu+e5C6Tl3zmjXCPfwLC1W/xA=</latexit> <latexit sha1_base64="VdTUT9ozay0Vmujujxr5ThUjYU=">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</latexit> <latexit sha1_base64="gWd/WLbOo7VpDFDPWdpOYq3ATY=">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</latexit> <latexit sha1_base64="gWd/WLbOo7VpDFDPWdpOYq3ATY=">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</latexit> <latexit sha1_base64="gWd/WLbOo7VpDFDPWdpOYq3ATY=">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</latexit> <latexit sha1_base64="gWd/WLbOo7VpDFDPWdpOYq3ATY=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="54xB9bxtl9GBQXUhdlwANDpb6Gk=">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</latexit> <latexit sha1_base64="GuI8fsOd9wJRsKsvcd5jbcTFQS4=">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</latexit> <latexit sha1_base64="GuI8fsOd9wJRsKsvcd5jbcTFQS4=">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</latexit> <latexit sha1_base64="GuI8fsOd9wJRsKsvcd5jbcTFQS4=">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</latexit> <latexit sha1_base64="GuI8fsOd9wJRsKsvcd5jbcTFQS4=">AClnicbVFRaxNBEN6cVWu0muqL4MtiKrRQwl0R7EulKJvjaVpC8kR5jZz6dK9vevuXDVd8if6a/q/8J/4971kCZ1YNmPb7ZnfkmKZS0FIZ/WsGDlYePHq8+aT9tvb8RWf95bHNSyNwIHKVm9MELCqpcUCSFJ4WBiFLFJ4k5+r/MklGitzfUSzAuMplqmUgB5atzZ3jYvBqpfMo1r65RakA4XUMrpxnMXZOeb2MO92wF9bB74OoAV3WRH+83jocTXJRZqhJKLB2GIUFxQ4MSaFw3h6VFgsQ5zDFoYcaMrSxq8ea83emfA0N/5o4jV7t8JBZu0sS7wyAzqzy7mK/F9uWFK6Gzupi5JQi9uP0lJxynlEZ9Ig4LUzAMQRvpeuTgDbwx5JxdeItpLQVncrgujPTIlxk7JBP2EemnASzAXZeyu5PtF/p8dhp/0M+67wXFURS7yoOq27bfQrTs+X1wvNOLwl70fae7/6nZxyp7w96yTRaxD2yfWN9NmCXbMb9ov9Dl4H4MvwdbadBqal6xhQj6fwGIkc38</latexit> <latexit sha1_base64="Q7vZPcU1eDo3uqCgIZYeor7CQd4=">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</latexit> <latexit sha1_base64="Q7vZPcU1eDo3uqCgIZYeor7CQd4=">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</latexit> <latexit sha1_base64="Q7vZPcU1eDo3uqCgIZYeor7CQd4=">ACdHicbVHLSgMxFE3Hd31VXeoiWAUFKTNF0I0gunHng1aFdpBMeqeGZjJjcketg7/hVn/LH3FtZlrEVi8EDuem5x7EiRSGHTdz5IzMTk1PTM7V5fWFxarqysXps41RyaPJaxvg2YASkUNFGghNtEA4sCTdB7zTv3zyCNiJWDewn4Eesq0QoOENLtbfOd17aMu5Stbt1V6m6Nbco+hd4Q1Alw7q4WyldtTsxTyNQyCUzpuW5CfoZ0yi4hNdyOzWQMN5jXWhZqFgExs8K06902zIdGsbaHoW0YH9PZCwyph8FVhkxvDfjvZz8r9dKMTz0M6GSFEHxwUNhKinGNE+AdoQGjrJvAeNaWK+U3zPNONqcRm5CPAqZNLBXDHpHqFPwMykCsBuqsQUfmX5I/exF7I/yP3I/U/CEz4XvEUXD87M8g9xt2f6CN575X3Bdr3luzbusV49Phv8xS9bJtkhHjkgx+SMXJAm4SQhb+SdfJS+nA2n6mwPpE5pOLNGRsqpfQNiI8DF</latexit> <latexit sha1_base64="Q7vZPcU1eDo3uqCgIZYeor7CQd4=">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</latexit> <latexit sha1_base64="cyr484ZtkEmTSJLlVvzsSyal0aU=">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</latexit> <latexit sha1_base64="cyr484ZtkEmTSJLlVvzsSyal0aU=">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</latexit> <latexit sha1_base64="cyr484ZtkEmTSJLlVvzsSyal0aU=">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</latexit> <latexit sha1_base64="cyr484ZtkEmTSJLlVvzsSyal0aU=">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</latexit> <latexit sha1_base64="/El4wQruEgLNQ2TjZy08Ka+ntoY=">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</latexit> <latexit sha1_base64="/El4wQruEgLNQ2TjZy08Ka+ntoY=">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</latexit> <latexit sha1_base64="/El4wQruEgLNQ2TjZy08Ka+ntoY=">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</latexit> <latexit sha1_base64="/El4wQruEgLNQ2TjZy08Ka+ntoY=">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</latexit> <latexit sha1_base64="h+rx6DJSa5Y1f/lVzQ9bSJ/61U=">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</latexit> <latexit sha1_base64="h+rx6DJSa5Y1f/lVzQ9bSJ/61U=">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</latexit> <latexit sha1_base64="h+rx6DJSa5Y1f/lVzQ9bSJ/61U=">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</latexit> <latexit sha1_base64="h+rx6DJSa5Y1f/lVzQ9bSJ/61U=">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</latexit> <latexit sha1_base64="cyr484ZtkEmTSJLlVvzsSyal0aU=">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</latexit> <latexit sha1_base64="cyr484ZtkEmTSJLlVvzsSyal0aU=">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</latexit> <latexit sha1_base64="cyr484ZtkEmTSJLlVvzsSyal0aU=">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</latexit> <latexit sha1_base64="cyr484ZtkEmTSJLlVvzsSyal0aU=">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</latexit> <latexit sha1_base64="GKLErO3sLKuTdwhNwrxTCDklzg=">ACcHicbVHbSsNAEN3Ge71WXwQfXK2CiJREBH0RF98VLFaINstpN2cbOJu5NqDf6Er/pj/oZf4CYWsdWBhcOZM7NnZoJECoOu+1FyxsYnJqemZ8qzc/MLi0uV5RsTp5pDncy1o2AGZBCQR0FSmgkGlgUSLgN7s/y/G0PtBGxusZ+An7EOkqEgjO0VGOrJeMOfd6W6q6NbcI+hd4A1Alg7i4q5SuWu2YpxEo5JIZ0/TcBP2MaRcwku5lRpIGL9nHWhaqFgExs8Kwy902zJtGsbaPoW0YH9XZCwyph8FVhkx7JrRXE7+l2umGB75mVBJiqD490dhKinGNJ+etoUGjrJvAeNaWK+Ud5lmHO2OhjohHodMGtgrCr1j1Cn4mRQB2AnVyIA9ph9SP3sWB8P8j9zPFDziU+F7SHt+Vm+g9xt2V7BG935X3CzX/Pcmne5Xz05HdxjmqyRTbJDPHJITsg5uSB1wokr+SNvJc+nVn3dn4ljqlQc0KGQpn9wufsb+P</latexit> <latexit sha1_base64="GKLErO3sLKuTdwhNwrxTCDklzg=">ACcHicbVHbSsNAEN3Ge71WXwQfXK2CiJREBH0RF98VLFaINstpN2cbOJu5NqDf6Er/pj/oZf4CYWsdWBhcOZM7NnZoJECoOu+1FyxsYnJqemZ8qzc/MLi0uV5RsTp5pDncy1o2AGZBCQR0FSmgkGlgUSLgN7s/y/G0PtBGxusZ+An7EOkqEgjO0VGOrJeMOfd6W6q6NbcI+hd4A1Alg7i4q5SuWu2YpxEo5JIZ0/TcBP2MaRcwku5lRpIGL9nHWhaqFgExs8Kwy902zJtGsbaPoW0YH9XZCwyph8FVhkx7JrRXE7+l2umGB75mVBJiqD490dhKinGNJ+etoUGjrJvAeNaWK+Ud5lmHO2OhjohHodMGtgrCr1j1Cn4mRQB2AnVyIA9ph9SP3sWB8P8j9zPFDziU+F7SHt+Vm+g9xt2V7BG935X3CzX/Pcmne5Xz05HdxjmqyRTbJDPHJITsg5uSB1wokr+SNvJc+nVn3dn4ljqlQc0KGQpn9wufsb+P</latexit> <latexit sha1_base64="GKLErO3sLKuTdwhNwrxTCDklzg=">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</latexit> <latexit sha1_base64="GKLErO3sLKuTdwhNwrxTCDklzg=">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</latexit> <latexit sha1_base64="Wkh1sY0r8KS9myLI53ZpDYRNR0=">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</latexit> <latexit sha1_base64="Wkh1sY0r8KS9myLI53ZpDYRNR0=">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</latexit> <latexit sha1_base64="Wkh1sY0r8KS9myLI53ZpDYRNR0=">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</latexit> <latexit sha1_base64="Wkh1sY0r8KS9myLI53ZpDYRNR0=">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</latexit> <latexit sha1_base64="aINBFHga2hUicysK4Dil3fuyl8=">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</latexit> <latexit sha1_base64="aINBFHga2hUicysK4Dil3fuyl8=">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</latexit> <latexit sha1_base64="aINBFHga2hUicysK4Dil3fuyl8=">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</latexit> <latexit sha1_base64="aINBFHga2hUicysK4Dil3fuyl8=">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</latexit> <latexit sha1_base64="/KGc5rGgrVgv+3z8TAswGdcwQ6M=">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</latexit> <latexit sha1_base64="/KGc5rGgrVgv+3z8TAswGdcwQ6M=">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</latexit> <latexit sha1_base64="/KGc5rGgrVgv+3z8TAswGdcwQ6M=">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</latexit> <latexit sha1_base64="/KGc5rGgrVgv+3z8TAswGdcwQ6M=">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</latexit> <latexit sha1_base64="3JpsgJfo8VOCHarwkSPUTqEw=">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</latexit> <latexit sha1_base64="3JpsgJfo8VOCHarwkSPUTqEw=">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</latexit> <latexit sha1_base64="3JpsgJfo8VOCHarwkSPUTqEw=">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</latexit> <latexit sha1_base64="3JpsgJfo8VOCHarwkSPUTqEw=">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</latexit> Block-trees size of the string n alphabet size σ log z z nodes Stop recursion when B d log σ e > d log n e log n log σ B = O ( log n / log σ ) z log n h = log n log σ log n log n log σ + z log n O ( z log n ) z log n At level i O ( z log n log n log σ = z log n ) bits nodes take t i O ( t i log n ) bits 16

  37. 2D Block-trees A hybrid between the k 2 -tree to exploit the clustering of the 0s Two-Dimensional Block Trees , and the block tree to exploit the Brisaboa, Gagie, Gómez-Brandón, Navarro , DCC 2018 repetitiveness of the adjacency matrix. A source block may overlap up to 4 adjacent blocks. 1 0 Target 1 0 1 0 Source 1 0 Credits to A. Gómez-Brandón 17

  38. 2D Block-trees A hybrid between the k 2 -tree to exploit the clustering of the 0s Two-Dimensional Block Trees , and the block tree to exploit the Brisaboa, Gagie, Gómez-Brandón, Navarro , DCC 2018 repetitiveness of the adjacency matrix. A source block may overlap up to 4 adjacent blocks. 1 0 Target 1 0 1 0 Source 1 0 Credits to A. Gómez-Brandón 17

  39. 2D Block-trees A hybrid between the k 2 -tree to exploit the clustering of the 0s Two-Dimensional Block Trees , and the block tree to exploit the Brisaboa, Gagie, Gómez-Brandón, Navarro , DCC 2018 repetitiveness of the adjacency matrix. A source block may overlap up to 4 adjacent blocks. Pointer (0,0) (1,0) Offset 1 0 Target 1 0 1 0 Source 1 0 (0,1) (1,1) Credits to A. Gómez-Brandón 17

  40. 2D Block-trees 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 18

  41. 2D Block-trees 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 18

  42. 2D Block-trees 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 (0,0) 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 18

  43. 2D Block-trees 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 (0,0) 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 18

  44. 2D Block-trees 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 (0,0) 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 (0,0) 0 1 0 0 0 1 0 0 18

  45. 2D Block-trees 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 (0,0) 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 (0,0) 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 18

  46. 2D Block-trees 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 (0,0) 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 (0,0) (0,0) 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 18

  47. 2D Block-trees 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 (0,0) 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 (0,0) (0,0) 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 18

  48. 2D Block-trees 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 (0,0) 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 (0,0) (0,0) 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 18

  49. 2D Block-trees 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 (0,0) 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 (0,0) (0,0) 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 18

  50. 2D Block-trees 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 (0,0) 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 (0,0) (0,0) (0,1) 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 18

  51. 2D Block-trees 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 (0,0) 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 (0,0) (0,0) (0,1) 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 18

  52. 2D Block-trees 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 (0,0) 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 (0,0) (0,0) (0,0) (0,0) (0,1) (0,0) (0,0) 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 18

  53. 2D Block-trees 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 On Web graphs, we 1 1 0 0 1 1 0 0 are not exploiting the 0 1 0 0 0 1 0 0 “empty” zones 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 of zeroes as k 2 -trees. 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 (0,0) 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 (0,0) (0,0) (0,0) (0,0) (0,1) (0,0) (0,0) 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 18

  54. 2D Block-trees on Web graphs 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 (0,0) 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,1) 0 1 0 0 0 1 1 0 1 0 19

  55. 2D Block-trees on Web graphs 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 Introduce a new 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 type of node to 0 0 0 0 0 0 0 0 mark empty zones. 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 (0,0) 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,1) 0 1 0 0 0 1 1 0 1 0 19

  56. 2D Block-trees on Web graphs 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 (0,0) 1 1 0 0 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 0 1 1 0 0 1 0 (0,1) 0 1 0 1 1 0 1 0 20

  57. 2D Block-trees on Web graphs 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 (0,0) 1 1 0 0 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 0 1 1 0 0 1 0 (0,1) 0 1 0 1 1 0 1 0 21

  58. 2D Block-trees on Web graphs 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 T 1010 1010 1010 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 (0,0) 1 1 0 0 1 0 0 1 L 0001 1101 0010 1010 0 1 0 0 1 0 1 1 0 0 0 0 0 1 1 0 0 1 0 (0,1) 0 1 0 1 1 0 1 0 21

  59. 2D Block-trees on Web graphs 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 T 1010 1010 1010 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 (0,0) 1 1 0 0 1 0 0 1 L 0001 1101 0010 1010 0 1 0 0 1 0 1 1 N 100001 0 0 0 0 0 1 1 0 0 1 0 (0,1) 0 1 0 1 1 0 1 0 21

  60. 2D Block-trees on Web graphs 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 T 1010 1010 1010 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 (0,0) 1 1 0 0 1 0 0 1 L 0001 1101 0010 1010 0 1 0 0 1 0 1 1 N 100001 P 1 1 O 1 00 0 0 0 0 0 1 1 0 0 1 0 (0,1) 0 1 0 1 1 0 1 0 21

  61. 2D Block-trees on Web graphs 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 T 1010 1010 1010 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 (0,0) 1 1 0 0 1 0 0 1 L 0001 1101 0010 1010 0 1 0 0 1 0 1 1 N 100001 P 1 1 O 1 00 0 0 0 0 0 1 1 0 0 1 0 (0,1) 0 1 0 1 1 0 1 0 P 2 7 O 2 01 21

  62. 2D Block-trees on Web graphs 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 Access 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 T 1010 1010 1010 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 (0,0) 1 1 0 0 1 0 0 1 L 0001 1101 0010 1010 0 1 0 0 1 0 1 1 N 100001 P 1 1 O 1 00 0 0 0 0 0 1 1 0 0 1 0 (0,1) 0 1 0 1 1 0 1 0 P 2 7 O 2 01 21

  63. 2D Block-trees on Web graphs 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 Access 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 T 1010 1010 1010 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 (0,0) 1 1 0 0 1 0 0 1 L 0001 1101 0010 1010 0 1 0 0 1 0 1 1 N 100001 P 1 1 O 1 00 0 0 0 0 0 1 1 0 0 1 0 (0,1) 0 1 0 1 1 0 1 0 P 2 7 O 2 01 21

  64. 2D Block-trees on Web graphs 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 Access 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 T 1010 1010 1010 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 (0,0) 1 1 0 0 1 0 0 1 L 0001 1101 0010 1010 0 1 0 0 1 0 1 1 N 100001 P 1 1 O 1 00 0 0 0 0 0 1 1 0 0 1 0 (0,1) 0 1 0 1 1 0 1 0 P 2 7 O 2 01 21

  65. 2D Block-trees on Web graphs 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 Access 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 T 1010 1010 1010 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 (0,0) 1 1 0 0 1 0 0 1 L 0001 1101 0010 1010 0 1 0 0 1 0 1 1 N 100001 P 1 1 O 1 00 0 0 0 0 0 1 1 0 0 1 0 (0,1) 0 1 0 1 1 0 1 0 P 2 7 O 2 01 21

  66. 2D Block-trees on Web graphs 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 Access 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 T 1010 1010 1010 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 (0,0) 1 1 0 0 1 0 0 1 L 0001 1101 0010 1010 0 1 0 0 1 0 1 1 N 100001 P 1 1 O 1 00 0 0 0 0 0 1 1 0 0 1 0 (0,1) 0 1 0 1 1 0 1 0 P 2 7 O 2 01 21

  67. 2D Block-trees on Web graphs 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 Access 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 T 1010 1010 1010 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 (0,0) 1 1 0 0 1 0 0 1 L 0001 1101 0010 1010 0 1 0 0 1 0 1 1 N 100001 1 P 1 1 O 1 00 0 0 0 0 0 1 1 0 0 1 0 (0,1) 0 1 0 1 1 0 1 0 P 2 7 O 2 01 21

  68. 2D Block-trees on Web graphs 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 Access 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 T 1010 1010 1010 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 (0,0) 1 1 0 0 1 0 0 1 L 0001 1101 0010 1010 0 1 0 0 1 0 1 1 N 100001 1 P 1 1 O 1 00 0 0 0 0 0 1 1 0 0 1 0 (0,1) 0 1 0 1 1 0 1 0 P 2 7 O 2 01 21

  69. 2D Block-trees on Web graphs 22

  70. 2D Block-trees on Web graphs Up to 50% reduction wrt the k 2 -tree. 22

Recommend

8.3 GRAPH REPRESENTATIONS AND GRAPH ISOMORPHISM INCIDENCE TABLE REPRESENTATION def: An incidence

8.3 GRAPH REPRESENTATIONS AND GRAPH ISOMORPHISM INCIDENCE TABLE REPRESENTATION def: An incidence

8.3.1 Section 8.3 Graph Representations and Graph Isomorphism 8.3 GRAPH REPRESENTATIONS AND GRAPH ISOMORPHISM INCIDENCE TABLE REPRESENTATION def: An incidence table for a graph has a column indexed by each edge. The entries in the

335 views • 11 slides
1 Last week we talked about implicit graph representations. This week we're going to be

1 Last week we talked about implicit graph representations. This week we're going to be

1 Last week we talked about implicit graph representations. This week we're going to be implementing Prim's Algorithm in two different ways to practice working with explicit graph representations, namely, adjacency matrices and adjacency lists.

208 views • 18 slides
Parsing of natural language sentences to syntactic and semantic graph representations

Parsing of natural language sentences to syntactic and semantic graph representations

Parsing of natural language sentences to syntactic and semantic graph representations Abschlussvortrag zum Forschungsprojekt Pius Meinert April 13, 2018 Overview Graph Representations Corpora Parsing Techniques Parser 1 Overview Graph

819 views • 57 slides
CSE 326: Data Structures Graph representations Graphs Topological Sort Topological

CSE 326: Data Structures Graph representations Graphs Topological Sort Topological

Agenda Basic graph terminology CSE 326: Data Structures Graph representations Graphs Topological Sort Topological sort Reference: Weiss, Ch. 9 Hal Perkins Spring 2007 Lectures 22-23 2 Some Applications: Graph ADT?

332 views • 6 slides
Graphs and their representations After this lesson, you should be able to explain what

Graphs and their representations After this lesson, you should be able to explain what

Graphs and their representations After this lesson, you should be able to explain what makes a graph different than a tree implement simple graph algorithms https://www.google.com/maps/preview#!data=!1m4!1m3!1d989355!2d-

505 views • 15 slides
More refined representations Control dependence graph Problem: control-flow edges in CFG

More refined representations Control dependence graph Problem: control-flow edges in CFG

More refined representations Control dependence graph Problem: control-flow edges in CFG overspecify evaluation Program dependence graph (PDG): order data dependence graph + control dependence graph (CDG) [Ferrante, Ottenstein, &amp; Warren,

260 views • 5 slides
Graph Algorithms Graphs Nodes/vertexes: Edges: (undirected) (directed) b a Representations

Graph Algorithms Graphs Nodes/vertexes: Edges: (undirected) (directed) b a Representations

Graph Algorithms Graphs Nodes/vertexes: Edges: (undirected) (directed) b a Representations of graph G with vertices V and edges E c (u, v) E V x V adjacency-matrix A: A u, v = 1 a b c Size: |V| 2 a 0 1 0 b 1 0 1

964 views • 78 slides
What The HELK? Enabling Graph Analytics for Effective Threat Hunting HELK THP OSSEM Agenda

What The HELK? Enabling Graph Analytics for Effective Threat Hunting HELK THP OSSEM Agenda

What The HELK? Enabling Graph Analytics for Effective Threat Hunting HELK THP OSSEM Agenda Effective Threat Hunting? Current state of threat hunting programs Graph Theory Definition Origins Types Graph

1.69k views • 75 slides
Relational Pooling for Graph Representations Ryan L. Murphy 1 (with Balasubramaniam Srinivasan 2 ,

Relational Pooling for Graph Representations Ryan L. Murphy 1 (with Balasubramaniam Srinivasan 2 ,

Relational Pooling for Graph Representations Ryan L. Murphy 1 (with Balasubramaniam Srinivasan 2 , Vinayak Rao 1 , Bruno Ribeiro 2 ) 1 Department of Statistics 2 Department of Computer Science Purdue University, West Lafayette, IN, USA ArXiv 1

321 views • 9 slides
Learning Semantic Entity Representations with Knowledge Graph and Deep Neural Networks and its

Learning Semantic Entity Representations with Knowledge Graph and Deep Neural Networks and its

Learning Semantic Entity Representations with Knowledge Graph and Deep Neural Networks and its Application to Named Entity Disambiguation Hongzhao Huang 1 and Larry Heck 2 Computer Science Department, Rensselaer Polytechnic Institute 1 Microsoft

243 views • 23 slides
GRAPH REPRESENTATIONS, BACKPROPAGATION AND BIOLOGICAL PLAUSIBILITY Marco Gori SAILAB,

GRAPH REPRESENTATIONS, BACKPROPAGATION AND BIOLOGICAL PLAUSIBILITY Marco Gori SAILAB,

GRAPH REPRESENTATIONS, BACKPROPAGATION AND BIOLOGICAL PLAUSIBILITY Marco Gori SAILAB, University of Siena NeurIPS 2019 OUTLINE Learning in structured domains Diffusion machines and spatiotemporal locality Backpropagation diffusion

849 views • 27 slides
Graph Representation and Traversals Mark Redekopp David Kempe Sandra Batista 2 GRAPH

Graph Representation and Traversals Mark Redekopp David Kempe Sandra Batista 2 GRAPH

1 CSCI 104 Graph Representation and Traversals Mark Redekopp David Kempe Sandra Batista 2 GRAPH REPRESENTATIONS 3 Graph Notation A graph is a collection of vertices h (or nodes) and edges that b c connect vertices a A vertex d

806 views • 26 slides
Learning Graph Representations for Video Understanding Xiaolong Wang Carnegie Mellon University

Learning Graph Representations for Video Understanding Xiaolong Wang Carnegie Mellon University

Learning Graph Representations for Video Understanding Xiaolong Wang Carnegie Mellon University Computer Vision Dog He et al. Mask R-CNN. ICCV 2017. Gler et al. DensePose: Dense Human Pose Estimation In The Wild. CVPR 2018. Deep Learning

941 views • 64 slides
Learning Lane Graph Representations for Motion Forecasting Ming Liang, Bin Yang, Rui Hu, Yun

Learning Lane Graph Representations for Motion Forecasting Ming Liang, Bin Yang, Rui Hu, Yun

Learning Lane Graph Representations for Motion Forecasting Ming Liang, Bin Yang, Rui Hu, Yun Chen, Renjie Liao, Song Feng, Raquel Urtasun HD Maps for Motion Forecasting Motion forecasting predicts future trajectories of actors given their past

378 views • 19 slides
Minimal Geometric Graph Representations of Order Types Oswin Aichholzer, Martin Balko, Michael

Minimal Geometric Graph Representations of Order Types Oswin Aichholzer, Martin Balko, Michael

Minimal Geometric Graph Representations of Order Types Oswin Aichholzer, Martin Balko, Michael Hoffmann, Jan Kyn cl, Wolfgang Mulzer, Irene Parada, Alexander Pilz, Manfred Scheucher, Pavel Valtr, Birgit Vogtenhuber, Emo Welzl 1 Order Types

558 views • 43 slides
Graphs and their representations After this lesson, you should be able to define the

Graphs and their representations After this lesson, you should be able to define the

Review Re A E C F B D Graphs and their representations After this lesson, you should be able to define the major terminology relating to graphs implement a graph in code, using various conventions https :// www.google.com /

567 views • 22 slides
Network modularity, currency metabolites and graph representations of metabolism Petter Holme

Network modularity, currency metabolites and graph representations of metabolism Petter Holme

metabolic networks, intro networks (physicist style?) modularity &amp; currency metabolites subnetwork hierarchies Network modularity, currency metabolites and graph representations of metabolism Petter Holme KTH, CSC, Computational Biology

1.54k views • 106 slides
Cartograms and Contact Representations: Applications of Schnyder Woods in Graph Drawing Ljubljana

Cartograms and Contact Representations: Applications of Schnyder Woods in Graph Drawing Ljubljana

Cartograms and Contact Representations: Applications of Schnyder Woods in Graph Drawing Ljubljana January 17, 2013 Stefan Felsner Technische Universit at Berlin felsner@math.tu-berlin.de Outline Cartograms: An Introduction Schnyder

798 views • 65 slides
CS141: Intermediate Data Structures and Algorithms Graphs Amr Magdy Graph Data Structure A set

CS141: Intermediate Data Structures and Algorithms Graphs Amr Magdy Graph Data Structure A set

CS141: Intermediate Data Structures and Algorithms Graphs Amr Magdy Graph Data Structure A set of nodes (vertices) and edges connecting them 2 Graph Applications Road network Social media networks Knowledge bases 3 Graph Representations

807 views • 66 slides
CS141: Intermediate Data Structures and Algorithms Graphs Amr Magdy Graph Data Structure A set

CS141: Intermediate Data Structures and Algorithms Graphs Amr Magdy Graph Data Structure A set

CS141: Intermediate Data Structures and Algorithms Graphs Amr Magdy Graph Data Structure A set of nodes (vertices) and edges connecting them 2 Graph Applications Road network Social media networks Knowledge basesS 3 Graph Representations

1.33k views • 73 slides
Graphs and their representations After this lesson, you should be able to define the

Graphs and their representations After this lesson, you should be able to define the

A E C F B D Graphs and their representations After this lesson, you should be able to define the major terminology relating to graphs implement a graph in code, using various conventions

233 views • 21 slides
Elementary Graph Algorithms [for graphs with no edge weights] Course: CS 5130 - Advanced Data

Elementary Graph Algorithms [for graphs with no edge weights] Course: CS 5130 - Advanced Data

Elementary Graph Algorithms [for graphs with no edge weights] Course: CS 5130 - Advanced Data Structures and Algorithms Instructor: Dr. Badri Adhikari Representations of graph A directed or undirected graph G = (V, E) can be represented as (a) a

778 views • 28 slides
Network modularity, currency metabolites representa- tions of and graph representations of

Network modularity, currency metabolites representa- tions of and graph representations of

Network modularity, currency metabolites and graph Network modularity, currency metabolites representa- tions of and graph representations of metabolism metabolism PETTER HOLME metabolic Petter Holme networks, intro networks KTH,

1.14k views • 111 slides
Graphs CS16: Introduction to Data Structures &amp; Algorithms Spring 2020 Outline What is a

Graphs CS16: Introduction to Data Structures &amp; Algorithms Spring 2020 Outline What is a

Graphs CS16: Introduction to Data Structures &amp; Algorithms Spring 2020 Outline What is a Graph Terminology Properties Graph Types Representations Performance BFS/DFS Applications 2 What is a Graph A graph

966 views • 60 slides

More recommend