Arad Neamt 366 Bucharest 0 87 Zerind 151 Craiova 160 75 - PowerPoint PPT Presentation

Straight−line distance Oradea to Bucharest 71 Arad Neamt 366 Bucharest 0 87 Zerind 151 Craiova 160 75 Dobreta 242 Iasi Eforie Arad 161 140 92 Fagaras 178 Sibiu Fagaras 99 Giurgiu 77 118 Hirsova 151 Vaslui 80 Iasi 226 Rimnicu Vilcea Lugoj 244 Timisoara Mehadia 241 142 211 111 Neamt 234 Pitesti 97 Lugoj Oradea 380 70 98 Pitesti 98 Hirsova 85 146 Rimnicu Vilcea 101 193 Mehadia Urziceni Sibiu 86 253 75 138 Timisoara Bucharest 329 120 Urziceni Dobreta 80 90 Vaslui 199 Craiova Eforie Giurgiu Zerind 374

Arad 366

Arad Sibiu Timisoara Zerind 253 329 374

Arad Sibiu Timisoara Zerind 329 374 Arad Fagaras Oradea Rimnicu Vilcea 366 176 380 193

Arad Sibiu Timisoara Zerind 329 374 Arad Fagaras Oradea Rimnicu Vilcea 366 380 193 Sibiu Bucharest 253 0

Arad 366=0+366

Arad Sibiu Timisoara Zerind 393=140+253 447=118+329 449=75+374

Arad Sibiu Timisoara Zerind 447=118+329 449=75+374 Arad Fagaras Oradea Rimnicu Vilcea 646=280+366 415=239+176 671=291+380 413=220+193

Arad Sibiu Timisoara Zerind 447=118+329 449=75+374 Arad Fagaras Oradea Rimnicu Vilcea 646=280+366 415=239+176 671=291+380 Craiova Pitesti Sibiu 526=366+160 417=317+100 553=300+253

Arad Sibiu Timisoara Zerind 447=118+329 449=75+374 Arad Fagaras Oradea Rimnicu Vilcea 646=280+366 671=291+380 Sibiu Bucharest Craiova Pitesti Sibiu 526=366+160 417=317+100 591=338+253 450=450+0 553=300+253

Arad Sibiu Timisoara Zerind 447=118+329 449=75+374 Fagaras Arad Oradea Rimnicu Vilcea 646=280+366 671=291+380 Sibiu Bucharest Craiova Pitesti Sibiu 526=366+160 591=338+253 450=450+0 553=300+253 Bucharest Craiova Rimnicu Vilcea 418=418+0 615=455+160 607=414+193

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Next: Example Up: l3 Previous: Optimality of A* IDA* Series of Depth-First Searches Like Iterative Deepening Search, except use A* cost threshold instead of depth threshold Ensures optimal solution queueing-fn is enqueue-at-front if f(child) threshold Threshold is h(root) for first pass Next threshold is f(min_child), where min_child is cutoff child with minimum f value This conservative increase ensures cannot look past optimal cost solution

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Next: RBFS Up: l3 Previous: Eight Puzzle Example Analysis Some redundant search, but small amount compared to work done on last iteration Dangerous if f values are very close If threshold = 21.1 and next value is 21.2, probably only include 1 new node each iteration Time: Space: SMA* search can be used to remember some nodes from one iteration to the next.

n c(n,a,n’) h(n) n’ h(n’) G

5 7 2 4 1 2 3 5 6 4 5 6 8 3 1 7 8 Start State Goal State

5 7 2 4 1 2 3 5 6 4 5 6 8 3 1 7 8 Start State Goal State