Asynch DP Example Asynch DP initial graph 1

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Asynch. DP Example

Asynch. DP Example

Asynch. DP: initial graph 1 1 a 1 s c 4 1 3 5

Asynch. DP: initial graph 1 1 a 1 s c 4 1 3 5 1 b 1 2 1 t 1 d 1 1 3

Asynch. DP: iteration 1 1 1 a 1 s c 4 1 3 5

Asynch. DP: iteration 1 1 1 a 1 s c 4 1 3 5 1 b 1 2 1 t 1 d 1 0 3

Asynch. DP: iteration 2 1 1 a 1 s c 4 1 3 5

Asynch. DP: iteration 2 1 1 a 1 s c 4 1 3 5 1 b 1 2 1 t 1 d 3 0 3

Asynch. DP: iteration 3 6 1 a 1 s c 4 1 3 5

Asynch. DP: iteration 3 6 1 a 1 s c 4 1 3 5 1 b 5 2 1 t 1 d 2 0 3

Asynch. DP: iteration 4 6 1 a 7 s c 4 1 3 5

Asynch. DP: iteration 4 6 1 a 7 s c 4 1 3 5 1 b 4 2 1 t 1 d 2 0 3

Asynch. DP: iteration 5 5 1 a 7 s c 4 1 3 5

Asynch. DP: iteration 5 5 1 a 7 s c 4 1 3 5 1 b 4 2 1 t 1 d 2 0 3

Asynch. DP: iteration 6 5 1 a 6 s c 4 1 3 5

Asynch. DP: iteration 6 5 1 a 6 s c 4 1 3 5 1 b 4 2 1 t 1 d 2 0 3

Asynch. DP: shortest path 5 1 a 6 s c 4 1 3 5

Asynch. DP: shortest path 5 1 a 6 s c 4 1 3 5 1 b 4 2 1 t 1 d 2 0 3

LRTA* Example

LRTA* Example

LRTA* - initialization 0 2 a 0 s c 2 2 2 3 0

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

LRTA* - trial 1 2 2 a 2 s c 2 2 2 3

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

LRTA* - trial 2 4 2 a 4 s c 2 2 2 3

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

LRTA* - trial 3 4 2 a 4 s c 2 2 2 3

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

LRTA* - trial 4 4 2 a 5 s c 2 2 2 3

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

LRTA* - trial 5 4 2 a 5 s c 2 2 2 3

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

LRTA*(2) Example

LRTA*(2) Example

LRTA*(2) - initialization 0 2 a 0 s c 2 2 2 3 0

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

LRTA*(2) – trial 1 2 2 a 2 s c 2 2 2 3

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

LRTA*(2) – trial 2 4 2 a 4 s c 2 2 2 3

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

LRTA*(2) – trial 3 4 2 a 5 s c 2 2 2 3

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

LRTA*(2) – trial 4 4 2 a 5 s c 2 2 2 3

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

Naive Assignment problem example #1

Naive Assignment problem example #1

Naive algorithm round p p p bidder preferre bid current assignment 1 2 3

Naive algorithm round p p p bidder preferre bid current assignment 1 2 3 d object incr. 0 0 1 x 2 2 (1, x 2) 1 0 2 x 2 2 (2, x 2) 2 0 4 0 3 x 3 1 (2, x 2), (3, x 3) 3 0 4 1 1 x 1 2 (1, x 1), (2, x 2), (3, x 3)

Naive Assignment Problem example #2

Naive Assignment Problem example #2

round p p p bidder preferred bid 1 2 3 object incr. current assignment

round p p p bidder preferred bid 1 2 3 object incr. current assignment 0 0 1 x 1 0 (1, x 1) 1 0 0 0 2 x 2 0 (1, x 1), (2, x 2) 2 0 0 0 3 x 1 0 (3, x 1), (2, x 2) 3 0 0 0 1 x 2 0 (3, x 1), (1, x 2) 4 0 0 0 2 x 1 0 (2, x 1), (1, x 2)

Improved Assignment Problem example #3

Improved Assignment Problem example #3

round p p p bidder preferred bid 1 2 3 object incr. current assignment

round p p p bidder preferred bid 1 2 3 object incr. current assignment 0 0 0 1 x 1 (1, x 1) 1 2 0 2 x 2 2 (1, x 1), (2, x 2) 2 3 2 0 3 x 1 2 (3, x 1), (2, x 2) 3 3 4 0 1 x 2 2 (3, x 1), (1, x 2) 4 5 4 0 2 x 1 2 (2, x 1), (1, x 2)

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