1. STRUCTURES AND STRATEGIES FOR STATE SPACE SEARCH 3 3.0Introduction 3.1Graph Theory 3.2Strategies for State Space Search 3.3Using the State Space to Represent Reasoning with the Predicate Calculus 3.4Epilogue and References 3.5Exercises Slide 3.1

2. A R T I F I C I A L I N T E L L I G E N C E: Structure and Strategies for Complex Problem Solving, 4th Edition George F. Luger © 2002 Addison Wesley Slide 3.2 Figure 3.1: The city of Königsberg.

3. A R T I F I C I A L I N T E L L I G E N C E: Structure and Strategies for Complex Problem Solving, 4th Edition George F. Luger © 2002 Addison Wesley Slide 3.3 Figure 3.2: Graph of the Königsberg bridge system.

4. A R T I F I C I A L I N T E L L I G E N C E: Structure and Strategies for Complex Problem Solving, 4th Edition George F. Luger © 2002 Addison Wesley Slide 3.4 Figure 3.3: A labeled directed graph.

5. A R T I F I C I A L I N T E L L I G E N C E: Structure and Strategies for Complex Problem Solving, 4th Edition George F. Luger © 2002 Addison Wesley Slide 3.5 Figure 3.4: A rooted tree, exemplifying family relationships.

6. A R T I F I C I A L I N T E L L I G E N C E: Structure and Strategies for Complex Problem Solving, 4th Edition George F. Luger © 2002 Addison Wesley Slide 3.6

7. A R T I F I C I A L I N T E L L I G E N C E: Structure and Strategies for Complex Problem Solving, 4th Edition George F. Luger © 2002 Addison Wesley Slide 3.7

8. A R T I F I C I A L I N T E L L I G E N C E: Structure and Strategies for Complex Problem Solving, 4th Edition George F. Luger © 2002 Addison Wesley Slide 3.8 Figure 3.6: State space of the 8-puzzle generated by “move blank” operations.

9. A R T I F I C I A L I N T E L L I G E N C E: Structure and Strategies for Complex Problem Solving, 4th Edition George F. Luger © 2002 Addison Wesley Slide 3.9 Figure 3.7: An instance of the traveling salesperson problem.

10. A R T I F I C I A L I N T E L L I G E N C E: Structure and Strategies for Complex Problem Solving, 4th Edition George F. Luger © 2002 Addison Wesley Slide 3.10 Figure 3.8: Search of the traveling salesperson problem. Each arc is marked with the total weight of all paths from the start node (A) to its endpoint.

11. A R T I F I C I A L I N T E L L I G E N C E: Structure and Strategies for Complex Problem Solving, 4th Edition George F. Luger © 2002 Addison Wesley Slide 3.11 Figure 3.9:An instance of the traveling salesperson problem with the nearest neighbor path in bold. Note that this path (A, E, D, B, C, A), at a cost of 550, is not the shortest path. The comparatively high cost of arc (C, A) defeated the heuristic.

12. A R T I F I C I A L I N T E L L I G E N C E: Structure and Strategies for Complex Problem Solving, 4th Edition George F. Luger © 2002 Addison Wesley Slide 3.12 Figure 3.10: State space in which goal-directed search effectively prunes extraneous search paths.

13. A R T I F I C I A L I N T E L L I G E N C E: Structure and Strategies for Complex Problem Solving, 4th Edition George F. Luger © 2002 Addison Wesley Slide 3.13 Figure 3.11: State space in which data-directed search prunes irrelevant data and their consequents and determines one of a number of possible goals.

14. A R T I F I C I A L I N T E L L I G E N C E: Structure and Strategies for Complex Problem Solving, 4th Edition George F. Luger © 2002 Addison Wesley Slide 3.14 Function backtrack algorithm

15. A R T I F I C I A L I N T E L L I G E N C E: Structure and Strategies for Complex Problem Solving, 4th Edition George F. Luger © 2002 Addison Wesley Slide 3.15 A trace of backtrack on the graph of figure 3.12

16. A R T I F I C I A L I N T E L L I G E N C E: Structure and Strategies for Complex Problem Solving, 4th Edition George F. Luger © 2002 Addison Wesley Slide 3.16 Figure 3.12: Backtracking search of a hypothetical state space.

17. A R T I F I C I A L I N T E L L I G E N C E: Structure and Strategies for Complex Problem Solving, 4th Edition George F. Luger © 2002 Addison Wesley Slide 3.17 Figure 3.13: Graph for breadth- and depth-first search examples.

18. A R T I F I C I A L I N T E L L I G E N C E: Structure and Strategies for Complex Problem Solving, 4th Edition George F. Luger © 2002 Addison Wesley Slide 3.18 Function breadth_first search algorithm

19. A R T I F I C I A L I N T E L L I G E N C E: Structure and Strategies for Complex Problem Solving, 4th Edition George F. Luger © 2002 Addison Wesley Slide 3.19 A trace of breadth_first_search on the graph of Figure 3.13