the book embedding problem from a sat solving perspective
play

The Book Embedding Problem from a SAT-Solving Perspective [GD 2015] - PowerPoint PPT Presentation

Jul 15, 2023 •354 likes •1.48k views

The Book Embedding Problem from a SAT-Solving Perspective [GD 2015] Michalis Bekos, Michael Kaufmann, Christian Zielke Universit at T ubingen, Germany The Book Embedding problem Vertices V ordered, on a spine Edges E assigned

  1. SAT formulation General idea: build formula F ( G , p ) via � 1. 1. ensure a proper order of the vertices on the spine σ ( v i , v j ) v i v j � 2. 2. assure that every edge is assigned to one of p pages e i e j χ ( e i , e j ) 3. 3. forbid crossings on each page e i e j forbid χ ( e i , e j ) together with

  2. SAT formulation General idea: build formula F ( G , p ) via � 1. 1. ensure a proper order of the vertices on the spine σ ( v i , v j ) v i v j � 2. 2. assure that every edge is assigned to one of p pages e i e j χ ( e i , e j ) 3. 3. forbid crossings on each page e i e j forbid χ ( e i , e j ) together with σ ( v i , v k ), σ ( v k , v j ), σ ( v j , v l ) v i v k v j v l

  3. SAT formulation General idea: build formula F ( G , p ) via � 1. 1. ensure a proper order of the vertices on the spine σ ( v i , v j ) v i v j � 2. 2. assure that every edge is assigned to one of p pages e i e j χ ( e i , e j ) � 3. 3. forbid crossings on each page e i e j forbid χ ( e i , e j ) together with σ ( v i , v k ), σ ( v k , v j ), σ ( v j , v l ) v i v k v j v l (for every pair of edges 8 forbidden configurations)

  4. SAT formulation General idea: build formula F ( G , p ) via � 1. 1. ensure a proper order of the vertices on the spine σ ( v i , v j ) v i v j � 2. 2. assure that every edge is assigned to one of p pages e i e j χ ( e i , e j ) � 3. 3. forbid crossings on each page solve optimization problem: F ( G , k − 1) is UNSAT , F ( G , k ) is SAT

  5. Experiments Setup: all Rome and North graphs (taken from www.graphdrawing.org)

  6. Experiments Setup: all Rome and North graphs (taken from www.graphdrawing.org) Timeout: 1200 sec

  7. Experiments Setup: all Rome and North graphs (taken from www.graphdrawing.org) Timeout: 1200 sec Rome graphs planar: 3281 nonplanar: 8253 (graphs are very sparse: 0.069)

  8. Experiments Setup: all Rome and North graphs (taken from www.graphdrawing.org) Timeout: 1200 sec Rome graphs planar: 3281 all fit in 2 pages nonplanar: 8253 all fit in 3 pages (graphs are very sparse: 0.069)

  9. Experiments Setup: all Rome and North graphs (taken from www.graphdrawing.org) Timeout: 1200 sec Rome graphs planar: 3281 all fit in 2 pages nonplanar: 8253 all fit in 3 pages (graphs are very sparse: 0.069) North graphs planar: 854 nonplanar: 423 (graphs are denser: 0.13)

  10. Experiments Setup: all Rome and North graphs (taken from www.graphdrawing.org) Timeout: 1200 sec Rome graphs planar: 3281 all fit in 2 pages nonplanar: 8253 all fit in 3 pages (graphs are very sparse: 0.069) North graphs planar: 854 all fit in 2 pages nonplanar: 423 only 344 were solved completely (graphs are denser: 0.13)

  11. Experiments Setup: all Rome and North graphs (taken from www.graphdrawing.org) Timeout: 1200 sec Rome graphs planar: 3281 all fit in 2 pages nonplanar: 8253 all fit in 3 pages (graphs are very sparse: 0.069) North graphs planar: 854 all fit in 2 pages nonplanar: 423 only 344 were solved completely (some graphs have high book thickness) (graphs are denser: 0.13)

  12. Experiments Hypothesis: There is a (maximal) planar graph whose book thickness is 4.

  13. Experiments Hypothesis: There is a (maximal) planar graph whose book thickness is 4. Setup: several maximal planar graphs with 500-700 vertices

  14. Experiments Hypothesis: There is a (maximal) planar graph whose book thickness is 4. Setup: several maximal planar graphs with 500-700 vertices Construction: 1. triangulated graph as base (”skeleton”) 1. (not necessarily non-Hamiltonian)

  15. Experiments Hypothesis: There is a (maximal) planar graph whose book thickness is 4. Setup: several maximal planar graphs with 500-700 vertices Construction: 1. 1. triangulated graph as base (”skeleton”) (not necessarily non-Hamiltonian) 2. 2. augmenting the faces of the base graph by a combination of Stellation Octahedron Creation Graph Insertion

  16. Experiments Hypothesis: There is a (maximal) planar graph whose book thickness is 4. Setup: several maximal planar graphs with 500-700 vertices Construction: 1. 1. triangulated graph as base (”skeleton”) (not necessarily non-Hamiltonian) 2. 2. augmenting the faces of the base graph by a combination of Stellation Octahedron Creation Graph Insertion

  17. Experiments Hypothesis: There is a (maximal) planar graph whose book thickness is 4. Setup: several maximal planar graphs with 500-700 vertices Construction: 1. 1. triangulated graph as base (”skeleton”) (not necessarily non-Hamiltonian) 2. 2. augmenting the faces of the base graph by a combination of Stellation Octahedron Creation Graph Insertion

  18. Experiments Hypothesis: There is a (maximal) planar graph whose book thickness is 4. Setup: several maximal planar graphs with 500-700 vertices Construction: 1. 1. triangulated graph as base (”skeleton”) (not necessarily non-Hamiltonian) 2. 2. augmenting the faces of the base graph by a combination of Stellation Octahedron Creation Graph Insertion

  19. Experiments Hypothesis: There is a (maximal) planar graph whose book thickness is 4. Setup: several maximal planar graphs with 500-700 vertices Construction: 1. 1. triangulated graph as base (”skeleton”) (not necessarily non-Hamiltonian) 2. 2. augmenting the faces of the base graph by a combination of Stellation Octahedron Creation Graph Insertion

  20. Experiments Hypothesis: There is a (maximal) planar graph whose book thickness is 4. Setup: several maximal planar graphs with 500-700 vertices Construction: 1. 1. triangulated graph as base (”skeleton”) (not necessarily non-Hamiltonian) 2. 2. augmenting the faces of the base graph by a combination of Stellation Octahedron Creation Graph Insertion

  21. Experiments Hypothesis: There is a (maximal) planar graph whose book thickness is 4. Setup: several maximal planar graphs with 500-700 vertices Construction: 1. 1. triangulated graph as base (”skeleton”) (not necessarily non-Hamiltonian) 2. 2. augmenting the faces of the base graph by a combination of Stellation Octahedron Creation Graph Insertion

  22. Experiments Hypothesis: There is a (maximal) planar graph whose book thickness is 4. Setup: several maximal planar graphs with 500-700 vertices Construction: 1. 1. triangulated graph as base (”skeleton”) (not necessarily non-Hamiltonian) 2. 2. augmenting the faces of the base graph by a combination of Stellation Octahedron Creation Graph Insertion

  23. Experiments Hypothesis: There is a (maximal) planar graph whose book thickness is 4. Setup: several maximal planar graphs with 500-700 vertices (all 3 page embeddable) Construction: 1. 1. triangulated graph as base (”skeleton”) (not necessarily non-Hamiltonian) 2. 2. augmenting the faces of the base graph by a combination of Stellation Octahedron Creation Graph Insertion

  24. Experiments - Idea: possibly overcome the limit of ≈ 700 vertices

  25. Experiments - Idea: possibly overcome the limit of ≈ 700 vertices Hypotheses: There is a maximal planar graph G a that has at least one face f a whose edges cannot be on the same page in any book embedding on 3 pages.

  26. Experiments - Idea: possibly overcome the limit of ≈ 700 vertices Hypotheses: There is a maximal planar graph G a that has at least one face f a whose edges cannot be on the same page in any book embedding on 3 pages. test F ( G a , 3) ∪ { ( χ ( e i , e j ) ∧ χ ( e i , e k ) } ∀ f a = ( e i , e j , e k ) ∈ G a

  27. Experiments - Idea: possibly overcome the limit of ≈ 700 vertices Hypotheses: There is a maximal planar graph G a that has at least one face f a whose edges cannot be on the same page in any book embedding on 3 pages. test F ( G a , 3) ∪ { ( χ ( e i , e j ) ∧ χ ( e i , e k ) } ∀ f a = ( e i , e j , e k ) ∈ G a There is a maximal planar graph G c that has at least one face f c whose edges are on the same page in any book embedding on 3 pages.

  28. Experiments - Idea: possibly overcome the limit of ≈ 700 vertices Hypotheses: There is a maximal planar graph G a that has at least one face f a whose edges cannot be on the same page in any book embedding on 3 pages. test F ( G a , 3) ∪ { ( χ ( e i , e j ) ∧ χ ( e i , e k ) } ∀ f a = ( e i , e j , e k ) ∈ G a There is a maximal planar graph G c that has at least one face f c whose edges are on the same page in any book embedding on 3 pages. ∀ f c = ( e i , e j , e k ) ∈ G c test F ( G c , 3) ∪ ( ¬ χ ( e i , e j ) ∨ ¬ χ ( e i , e k ))

  29. Experiments - Idea: possibly overcome the limit of ≈ 700 vertices Hypotheses: There is a maximal planar graph G a that has at least one face f a whose edges cannot be on the same page in any book embedding on 3 pages. test F ( G a , 3) ∪ { ( χ ( e i , e j ) ∧ χ ( e i , e k ) } ∀ f a = ( e i , e j , e k ) ∈ G a There is a maximal planar graph G c that has at least one face f c whose edges are on the same page in any book embedding on 3 pages. ∀ f c = ( e i , e j , e k ) ∈ G c test F ( G c , 3) ∪ ( ¬ χ ( e i , e j ) ∨ ¬ χ ( e i , e k )) G c

  30. Experiments - Idea: possibly overcome the limit of ≈ 700 vertices Hypotheses: There is a maximal planar graph G a that has at least one face f a whose edges cannot be on the same page in any book embedding on 3 pages. test F ( G a , 3) ∪ { ( χ ( e i , e j ) ∧ χ ( e i , e k ) } ∀ f a = ( e i , e j , e k ) ∈ G a There is a maximal planar graph G c that has at least one face f c whose edges are on the same page in any book embedding on 3 pages. ∀ f c = ( e i , e j , e k ) ∈ G c test F ( G c , 3) ∪ ( ¬ χ ( e i , e j ) ∨ ¬ χ ( e i , e k )) f a is outer face G a G c

  31. Experiments - Idea: possibly overcome the limit of ≈ 700 vertices Hypotheses: There is a maximal planar graph G a that has at least one face f a whose edges cannot be on the same page in any book embedding on 3 pages. test F ( G a , 3) ∪ { ( χ ( e i , e j ) ∧ χ ( e i , e k ) } ∀ f a = ( e i , e j , e k ) ∈ G a There is a maximal planar graph G c that has at least one face f c whose edges are on the same page in any book embedding on 3 pages. ∀ f c = ( e i , e j , e k ) ∈ G c test F ( G c , 3) ∪ ( ¬ χ ( e i , e j ) ∨ ¬ χ ( e i , e k )) G a G a G c

  32. Experiments - Idea: possibly overcome the limit of ≈ 700 vertices Hypotheses: There is a maximal planar graph G a that has at least one face f a whose edges cannot be on the same page in any book embedding on 3 pages. test F ( G a , 3) ∪ { ( χ ( e i , e j ) ∧ χ ( e i , e k ) } ∀ f a = ( e i , e j , e k ) ∈ G a There is a maximal planar graph G c that has at least one face f c whose edges are on the same page in any book embedding on 3 pages. ∀ f c = ( e i , e j , e k ) ∈ G c test F ( G c , 3) ∪ ( ¬ χ ( e i , e j ) ∨ ¬ χ ( e i , e k )) G a tested ≈ 284,000 graphs G a G c with 60 to 125 vertices → 0 confirmed Hypotheses

  33. Experiments Hypothesis: There is a 1-planar graph whose book thickness is (at least) 4.

  34. Experiments Hypothesis: There is a 1-planar graph whose book thickness is (at least) 4. 5 8 1 4 2 3 6 7

  35. Experiments Hypothesis: There is a 1-planar graph whose book thickness is (at least) 4. 5 8 1 4 1 5 4 2 7 3 8 6 2 3 6 7

  36. Experiments Hypothesis: There is a 1-planar graph whose book thickness is (at least) 5.

  37. Experiments Hypothesis: There is a 1-planar graph whose book thickness is (at least) 5. Setup: all 2,098,675 planar quadrangulations with 25 vertices triconnected; min degree 3 → augment every face with two crossing edges

  38. Experiments Hypothesis: There is a 1-planar graph whose book thickness is (at least) 5. Setup: all 2,098,675 planar quadrangulations with 25 vertices (all 4 page embeddable) triconnected; min degree 3 → augment every face with two crossing edges

  39. Experiments Hypothesis: There is a 1-planar graph whose book thickness is (at least) 5. Setup: all 2,098,675 planar quadrangulations with 25 vertices (all 4 page embeddable) triconnected; min degree 3 → augment every face with two crossing edges

  40. Experiments Hypothesis: There is a 1-planar graph whose book thickness is (at least) 5. Setup: all 2,098,675 planar quadrangulations with 25 vertices (all 4 page embeddable) triconnected; min degree 3 → augment every face with two crossing edges 8312 random optimal 1-planar graphs with 50 − 155 vertices (all 4 page embeddable)

  41. Experiments Hypothesis: There is a 1-planar graph whose book thickness is (at least) 5. Setup: all 2,098,675 planar quadrangulations with 25 vertices (all 4 page embeddable) triconnected; min degree 3 → augment every face with two crossing edges 8312 random optimal 1-planar graphs with 50 − 155 vertices (all 4 page embeddable)

  42. Experiments Hypothesis: There is a (maximal) planar graph, which cannot be embedded in a book of 3 pages, if the subgraphs at each page must be acyclic.

  43. Experiments Hypothesis: There is a (maximal) planar graph, which cannot be embedded in a book of 3 pages, if the subgraphs at each page must be acyclic. (Heath used that for proving book thickness of 3 for planar 3-trees)

  44. Experiments Hypothesis: There is a (maximal) planar graph, which cannot be embedded in a book of 3 pages, if the subgraphs at each page must be acyclic. (Heath used that for proving book thickness of 3 for planar 3-trees) Setup: tested over 15,000 maximal planar graphs with 25 to 80 vertices

  45. Experiments Hypothesis: There is a (maximal) planar graph, which cannot be embedded in a book of 3 pages, if the subgraphs at each page must be acyclic. (Heath used that for proving book thickness of 3 for planar 3-trees) Setup: tested over 15,000 maximal planar graphs with 25 to 80 vertices Timeout: 1200 sec 70.78 % of graphs were solved ≤ 3 minutes 76.37 % of graphs were solved ≤ 20 minutes

  46. Experiments Hypothesis: There is a (maximal) planar graph, which cannot be embedded in a book of 3 pages, if the subgraphs at each page must be acyclic. (Heath used that for proving book thickness of 3 for planar 3-trees) Setup: tested over 15,000 maximal planar graphs with 25 to 80 vertices Timeout: 1200 sec 70.78 % of graphs were solved ≤ 3 minutes 76.37 % of graphs were solved ≤ 20 minutes → additional constraints to force acyclic subgraphs increase runtime

  47. Experiments Hypothesis: (weaker) There is a (maximal) planar graph, which cannot be embedded in a book of 3 pages, if the subgraphs at each page must be acyclic. subgraphs are trees on n − 1 vertices vertices not spanned by trees build a face (w.l.o.g. outer face)

  48. Experiments Hypothesis: (weaker) There is a (maximal) planar graph, which cannot be embedded in a book of 3 pages, if the subgraphs at each page must be acyclic. 16 subgraphs are trees on n − 1 vertices vertices not spanned by trees 15 build a face (w.l.o.g. outer face) 14 12 11 13 9 10 7 8 6 5 3 4 1 2

  49. Experiments Hypothesis: (weaker) There is a (maximal) planar graph, which cannot be embedded in a book of 3 pages, if the subgraphs at each page must be acyclic. 16 subgraphs are trees on n − 1 vertices vertices not spanned by trees 15 build a face (w.l.o.g. outer face) 14 12 11 13 9 → Schnyder decomposition 10 not always possible 7 8 6 5 3 4 1 2

  50. Open problems All Hypothesis are unproven!

  51. Open problems All Hypothesis are unproven! - 1: (maximal) planar graph that requires 4 pages

  52. Open problems All Hypothesis are unproven! - 1: (maximal) planar graph that requires 4 pages - 1a: (maximal) planar graph that requires unicolored face

  53. Open problems All Hypothesis are unproven! - 1: (maximal) planar graph that requires 4 pages - 1a: (maximal) planar graph that requires unicolored face - 1b: (maximal) planar graph that cannot have a unicolored face

  54. Open problems All Hypothesis are unproven! - 1: (maximal) planar graph that requires 4 pages - 1a: (maximal) planar graph that requires unicolored face - 1b: (maximal) planar graph that cannot have a unicolored face - 2: 1-planar graph that requires 5 pages

  55. Open problems All Hypothesis are unproven! - 1: (maximal) planar graph that requires 4 pages - 1a: (maximal) planar graph that requires unicolored face - 1b: (maximal) planar graph that cannot have a unicolored face - 2: 1-planar graph that requires 5 pages - 3: (maximal) planar graph, that requires cyclic subgraphs on pages

  56. Open problems All Hypothesis are unproven! - 1: (maximal) planar graph that requires 4 pages - 1a: (maximal) planar graph that requires unicolored face - 1b: (maximal) planar graph that cannot have a unicolored face - 2: 1-planar graph that requires 5 pages - 3: (maximal) planar graph, that requires cyclic subgraphs on pages Improve the Encoding!

  57. Open problems All Hypothesis are unproven! - 1: (maximal) planar graph that requires 4 pages - 1a: (maximal) planar graph that requires unicolored face - 1b: (maximal) planar graph that cannot have a unicolored face - 2: 1-planar graph that requires 5 pages - 3: (maximal) planar graph, that requires cyclic subgraphs on pages Improve the Encoding! - cope with graphs, that have a high number of vertices and edges

  58. Open problems All Hypothesis are unproven! - 1: (maximal) planar graph that requires 4 pages - 1a: (maximal) planar graph that requires unicolored face - 1b: (maximal) planar graph that cannot have a unicolored face - 2: 1-planar graph that requires 5 pages - 3: (maximal) planar graph, that requires cyclic subgraphs on pages Improve the Encoding! - cope with graphs, that have a high number of vertices and edges - cope with graphs, that have high book thickness

  59. Open problems All Hypothesis are unproven! - 1: (maximal) planar graph that requires 4 pages - 1a: (maximal) planar graph that requires unicolored face - 1b: (maximal) planar graph that cannot have a unicolored face - 2: 1-planar graph that requires 5 pages - 3: (maximal) planar graph, that requires cyclic subgraphs on pages Improve the Encoding! - cope with graphs, that have a high number of vertices and edges - cope with graphs, that have high book thickness Thanks!!!

  60. Random Graph Creation

  61. Random Graph Creation

  62. Random Graph Creation left-to-right sorting

  63. Random Graph Creation left-to-right sorting

  64. Random Graph Creation left-to-right sorting

  65. Random Graph Creation left-to-right sorting

  66. Random Graph Creation left-to-right sorting

  67. Random Graph Creation

Recommend

Problem-Solving with Only 28% of employers classify college graduates Think-Alouds problem

Problem-Solving with Only 28% of employers classify college graduates Think-Alouds problem

12/5/14 Analysis of the situation Problem-solving is viewed as necessary for success in STEM fields, with the American Chemical Society (ACS) going so far as to refer to problem-solving as the ultimate goal. Problem-Solving with

316 views • 4 slides
New Defence Perspective New Defence Perspective New Defence Perspective New Defence Perspective

New Defence Perspective New Defence Perspective New Defence Perspective New Defence Perspective

New Defence Perspective New Defence Perspective New Defence Perspective New Defence Perspective Innovative technology, knowledge, problem solving are critical for Canada and its allies to mitigate new threats, stay ahead of potential

469 views • 18 slides
Interpersonal Problem Solving Faryaneh Poursardar Virginia Tech Slides based on the Effective

Interpersonal Problem Solving Faryaneh Poursardar Virginia Tech Slides based on the Effective

CS 2104 Introduction to Problem Solving Interpersonal Problem Solving Faryaneh Poursardar Virginia Tech Slides based on the Effective Problem Solving book Thomas-Kilmann Conflict Mode Instrument The TKI indicates your general

278 views • 23 slides
Externalizing Faryaneh Poursardar Virginia Tech Slides based on the Effective Problem

Externalizing Faryaneh Poursardar Virginia Tech Slides based on the Effective Problem

CS 2104 Introduction to Problem Solving Heuristics for Problem Solving: Externalizing Faryaneh Poursardar Virginia Tech Slides based on the Effective Problem Solving book Heuristics for Problem Solving (in the small) Heuristic: A

628 views • 44 slides
MEET YOUR LIBRARIAN & LIBRARY GVHS LIBRARIAN Noun A PROBLEM - SOLVING , BOOK LOVING ,

MEET YOUR LIBRARIAN & LIBRARY GVHS LIBRARIAN Noun A PROBLEM - SOLVING , BOOK LOVING ,

MEET YOUR LIBRARIAN & LIBRARY GVHS LIBRARIAN Noun A PROBLEM - SOLVING , BOOK LOVING , INFORMATION HUNTING , AND SOURCE - CITING RESEARCH NERD NINJA , WITH A DASH OF CAT LADY ON THE SIDE . SCHOOL LIBRARY MONTH # AASLSLM 1 0 Are libraries

451 views • 13 slides
Problem solving and search Chapter 3 Chapter 3 1 Outline Problem-solving agents Problem

Problem solving and search Chapter 3 Chapter 3 1 Outline Problem-solving agents Problem

Revised by Hankui Zhuo, March 7, 2018 Problem solving and search Chapter 3 Chapter 3 1 Outline Problem-solving agents Problem types Problem formulation Example problems Basic search algorithms Chapter 3 2 Problem-solving

934 views • 70 slides
Parameterized Algorithms for Book-Embedding Problems Sujoy Bhore , Robert Ganian, Fabrizio

Parameterized Algorithms for Book-Embedding Problems Sujoy Bhore , Robert Ganian, Fabrizio

Parameterized Algorithms for Book-Embedding Problems Sujoy Bhore , Robert Ganian, Fabrizio Montecchiani, Martin N ollenburg Graph Drawing September 19, 2019 1/33 The Problem v 9 v 8 v 4 v 1 v 2 v 3 v 4 v 5 v 6 v 7 v 8 v 9 v 5 v 3 v 7 v 6 v

449 views • 33 slides
Gathering Information on the Problem Slides mainly adapted from Dr. Foglers Strategies for

Gathering Information on the Problem Slides mainly adapted from Dr. Foglers Strategies for

Gathering Information on the Problem Slides mainly adapted from Dr. Foglers Strategies for Creative Problem Solving book Department of Chemical Engineering, University of Michigan, Ann Arbor Dr Fogler 11/5/2017 1 Problem Solving in the

243 views • 22 slides
New Defence Perspective Innovative technology, knowledge, problem solving are critical for Canada

New Defence Perspective Innovative technology, knowledge, problem solving are critical for Canada

New Defence Perspective Innovative technology, knowledge, problem solving are critical for Canada and its allies to mitigate new threats, stay ahead of potential adversaries, and meet evolving defence and security needs, while generating

614 views • 24 slides
Introduction to Problem Solving Methods Faryaneh Poursardar Virginia Tech Slides based on the

Introduction to Problem Solving Methods Faryaneh Poursardar Virginia Tech Slides based on the

CS 2104 Introduction to Problem Solving Methods Faryaneh Poursardar Virginia Tech Slides based on the Problem Solving and Comprehension book some slides created by Layne T. Watson Learning is a skill Research has shown that Accuracy

422 views • 17 slides
CS 2104 Introduction to Problem Solving Test Your Mind Faryaneh Poursardar Virginia Tech Slides

CS 2104 Introduction to Problem Solving Test Your Mind Faryaneh Poursardar Virginia Tech Slides

CS 2104 Introduction to Problem Solving Test Your Mind Faryaneh Poursardar Virginia Tech Slides based on the Problem Solving and Comprehension book Goals: I ncrease the students power to analyze problems Learn to recognize and

1.41k views • 20 slides
Problem Solving and Search Chapter 3 Outline Problem-solving agents Problem formulation

Problem Solving and Search Chapter 3 Outline Problem-solving agents Problem formulation

Problem Solving and Search Chapter 3 Outline Problem-solving agents Problem formulation Example problems Basic search algorithms Problem-Solving Agents In the simplest case, an agent will: formulate (or be given) a goal and a

1.23k views • 95 slides
Last time: Problem-Solving Problem solving: Goal formulation Problem formulation

Last time: Problem-Solving Problem solving: Goal formulation Problem formulation

Last time: Problem-Solving Problem solving: Goal formulation Problem formulation (states, operators) Search for solution Problem formulation: Initial state ? ? ? ? 1 Last time: Problem-Solving Problem

361 views • 18 slides
Problem solving and search Chapter 3 Chapter 3 1 Outline Problem-solving agents Problem

Problem solving and search Chapter 3 Chapter 3 1 Outline Problem-solving agents Problem

Problem solving and search Chapter 3 Chapter 3 1 Outline Problem-solving agents Problem types Problem formulation Example problems Basic search algorithms Chapter 3 3 Problem-solving agents Restricted form of general

973 views • 64 slides
Problem solving and search Chapter 3 Chapter 3 1 Outline Problem-solving agents Problem

Problem solving and search Chapter 3 Chapter 3 1 Outline Problem-solving agents Problem

Problem solving and search Chapter 3 Chapter 3 1 Outline Problem-solving agents Problem types Problem formulation Example problems Basic search algorithms Chapter 3 2 Problem-solving agents Restricted form of general

1k views • 74 slides
Who Are These Companies? PSU Problem Solving Process Explore the problem-solving 1. Position

Who Are These Companies? PSU Problem Solving Process Explore the problem-solving 1. Position

Who Are These Companies? PSU Problem Solving Process Explore the problem-solving 1. Position context. Mission, Vision, Values 2. Sense Stakeholders Decision-making Models Impediments 3. Uncover 4. Solve 5. Build 6. Achieve

250 views • 7 slides
Who Are These Companies? PSU Problem Solving Process Explore the problem-solving 1. Position

Who Are These Companies? PSU Problem Solving Process Explore the problem-solving 1. Position

Who Are These Companies? PSU Problem Solving Process Explore the problem-solving 1. Position context. Mission, Vision, Values 2. Sense Stakeholders Decision-making Models Impediments 3. Uncover 4. Solve 5. Build 6. Achieve

240 views • 12 slides
Problem Solving Courts: What Are They, Do They Really Work, What Are Veterans Problem Solving

Problem Solving Courts: What Are They, Do They Really Work, What Are Veterans Problem Solving

Problem Solving Courts: What Are They, Do They Really Work, What Are Veterans Problem Solving Courts? Presentation to: State Administration and Veterans Affairs Committee Jeffrey N. Kushner-Statewide Drug Court Coordinator- Supreme

549 views • 28 slides
Reasoning Faryaneh Poursardar Virginia Tech Slides based on the Problem Solving and

Reasoning Faryaneh Poursardar Virginia Tech Slides based on the Problem Solving and

CS 2104 Introduction to Problem Solving Deductive and Hypothetical Reasoning Faryaneh Poursardar Virginia Tech Slides based on the Problem Solving and Comprehension book Deductive and Hypothetical Thinking The day before yesterday you

226 views • 18 slides
Verbal Reasoning Faryaneh Poursardar Virginia Tech Slides based on the Problem Solving and

Verbal Reasoning Faryaneh Poursardar Virginia Tech Slides based on the Problem Solving and

CS 2104 Introduction to Problem Solving Verbal Reasoning Faryaneh Poursardar Virginia Tech Slides based on the Problem Solving and Comprehension book some slides created by Layne T. Watson Verbal Reasoning Problems For this type of

323 views • 20 slides
Problem Solving & Algorithm Design 01-1 Problem solving The act of finding a solution

Problem Solving & Algorithm Design 01-1 Problem solving The act of finding a solution

Problem Solving & Algorithm Design 01-1 Problem solving The act of finding a solution to a perplexing, distressing, vexing, or unsettled question 01-2 How to Solve it Written by George Polya in 1945 01-3 How to Solve it

907 views • 31 slides
and problem-solving techniques 2 Some mathematical principles and problem-solving techniques

and problem-solving techniques 2 Some mathematical principles and problem-solving techniques

Problem Solving Skills (14021601-3 ) Part 2 Some mathematical principles and problem-solving techniques 2 Some mathematical principles and problem-solving techniques Invariant Principle 3 1 Gauss When Karl Friedrich Gauss was still in

1.11k views • 77 slides
What problem are we solving? What problem are we solving? T EXAS T ECHNOLOGY T ASK F ORCE Next

What problem are we solving? What problem are we solving? T EXAS T ECHNOLOGY T ASK F ORCE Next

T EXAS I NNOVATION A LLIANCE From Smart City to Smart State | Kristie Chin, UT Austin What problem are we solving? What problem are we solving? T EXAS T ECHNOLOGY T ASK F ORCE Next Generation Vehicles Information & Next Generation &

277 views • 6 slides
Solving Problems by Searching Chapter 3 Ch. 03 p.1/49 Outline Problem-solving agents

Solving Problems by Searching Chapter 3 Ch. 03 p.1/49 Outline Problem-solving agents

Solving Problems by Searching Chapter 3 Ch. 03 p.1/49 Outline Problem-solving agents Problem types Problem formulation Example problems Basic search algorithms Ch. 03 p.2/49 Problem-solving agents

1.4k views • 49 slides

More recommend