1. AsynchDP Example

2. a b c d s t 1 1 1 1 1 1 3 1 5 4 2 3 1 11 AsynchDP: initial graph

3. a b c d s t 1 1 1 1 1 0 3 1 5 4 2 3 1 11 AsynchDP: iteration 1

4. a b c d s t 1 1 1 3 1 0 3 1 5 4 2 3 1 11 AsynchDP: iteration 2

5. a b c d s t 1 6 52 1 0 3 1 5 4 2 3 1 11 AsynchDP: iteration 3

6. a b c d s t 7 6 42 1 0 3 1 5 4 2 3 1 11 AsynchDP: iteration 4

7. a b c d s t 7 5 42 1 0 3 1 5 4 2 3 1 11 AsynchDP: iteration 5

8. a b c d s t 6 5 42 1 0 3 1 5 4 2 3 1 11 AsynchDP: iteration 6

9. a b c d s t 6 5 42 1 0 3 1 5 4 2 3 1 11 AsynchDP: shortest path

10. LRTA* Example

11. LRTA* - initialization a b c d s t 0 0 0 0 0 0 2 2 3 2 3 5 1 23

12. LRTA* - trial 1 a b c d s t 2 2 2 0 1 0 2 2 3 2 3 5 1 23

13. LRTA* - trial 2 a b c d s t 4 4 2 0 1 0 2 2 3 2 3 5 1 23

14. LRTA* - trial 3 a b c d s t 4 4 3 4 1 0 2 2 3 2 3 5 1 23

15. LRTA* - trial 4 a b c d s t 5 4 3 4 1 0 2 2 3 2 3 5 1 23

16. LRTA* - trial 5 a b c d s t 5 4 3 4 1 0 2 2 3 2 3 5 1 23

17. LRTA*(2) Example

18. LRTA*(2) - initialization a b c d s t 0 0 0 0 0 0 2 2 3 2 3 5 1 23

19. LRTA*(2) – trial 1 a b c d s t 2 2 2 0 1 0 2 2 3 2 3 5 1 23

20. LRTA*(2) – trial 2 a b c d s t 4 4 3 4 1 0 2 2 3 2 3 5 1 23

21. LRTA*(2) – trial 3 a b c d s t 5 4 3 4 1 0 2 2 3 2 3 5 1 23

22. LRTA*(2) – trial 4 a b c d s t 5 4 3 4 1 0 2 2 3 2 3 5 1 23

23. Naive Assignment problem example #1

24. Naive algorithm (1,x 1 ), (2,x 2 ), (3,x 3 ) 2x1x1 11403 (2,x 2 ), (3,x 3 )1x3x3 30402 (2,x 2 )2x2x2 20201 (1,x 2 )2x2x2 10000 current assignmentbid incr. preferre d object bidde r p3p3 p2p2 p1p1 round

25. Naive Assignment Problem example #2

26. (2,x 1 ), (1,x 2 )0x1x1 20004 (3,x 1 ), (1,x 2 )0x2x2 10003 (3,x 1 ), (2,x 2 )0x1x1 30002 (1,x 1 ), (2,x 2 )0x2x2 20001 (1,x 1 )0x1x1 10000 current assignmentbid incr. preferred object bidde r p3p3 p2p2 p1p1 round

27. Improved Assignment Problem example #3

28. (2,x 1 ), (1,x 2 ) 22 x1x1 20  4 (3,x 1 ), (1,x 2 ) 22 x2x2 10  3 (3,x 1 ), (2,x 2 ) 22 x1x1 30  2 (1,x 1 ), (2,x 2 ) 22 x2x2 20   1 (1,x 1 )  x1x1 100  0 current assignmentbid incr. preferred object bidde r p3p3 p2p2 p1p1 round