Submodular Streaming in All Its Glory: Tight Approximation, Minimum - PowerPoint PPT Presentation

Submodular Streaming in All Its Glory: Tight Approximation, Minimum Memory and Low Adaptive Complexity Ehsan Kazemi 1 , Marko Mitrovic 1 , Morteza Zadimoghaddam 2 , Silvio Lattanzi 2 , Amin Karbasi 1 1 Yale University and 2 Google

Streaming Algorithms Many practical scenarios we need to use streaming algorithms: the data arrives at a very fast pace there is only time to read the data once random access to the entire data is not possible and only a small fraction of the data can be loaded to the main memory Video from “Britain’s Got Talent” Summary � 2

Streaming Algorithms Many practical scenarios we need to use streaming algorithms: the data arrives at a very fast pace there is only time to read the data once random access to the entire data is not possible and only a small fraction of the data can be loaded to the main memory Is it possible to summarize a massive data set “on the fly”, i.e., when at any point of time we have access only to a small fraction of data? Video from “Britain’s Got Talent” Summary � 2

Submodularity � 3

Submodularity s 3 s 1 s 1 s 2 s 2 s 4 A = { s 1 , s 2 } B = { s 1 , s 2 , s 3 , s 4 } � 3

Submodularity s 3 s 1 s 1 s 2 s 2 s 4 A = { s 1 , s 2 } B = { s 1 , s 2 , s 3 , s 4 } Submodularity � 3

Submodularity s 3 s 1 s 1 s s s 2 s 2 s 4 A = { s 1 , s 2 } B = { s 1 , s 2 , s 3 , s 4 } Submodularity ∀ A ⊆ B ⊆ V and s ∈ V \ B � 3

Submodularity s 3 s 1 s 1 s s s 2 s 2 s 4 A = { s 1 , s 2 } B = { s 1 , s 2 , s 3 , s 4 } Submodularity ∀ A ⊆ B ⊆ V and s ∈ V \ B � 3

Submodularity s 3 s 1 s 1 s s s 2 s 2 s 4 A = { s 1 , s 2 } B = { s 1 , s 2 , s 3 , s 4 } Submodularity ∀ A ⊆ B ⊆ V and s ∈ V \ B f ( A ∪ { s } ) − f ( A ) ≥ f ( B ∪ { s } ) − f ( B ) � 3

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