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Generalization of the Shortest Path Algorithm
Shortest Path Space
On the Optimality of Our Decision Strategy
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15 puzzle 500 node graphs ALGOL artificial intelligence average degree BEGIN bi-directional algorithm binary tree blue amoeba bubble sort calculate cardinality comparison method cardinality comparison strategy conceptually replaced cut-set Dantzig's decision rule dense graphs density Dijkstra algorithm Dijkstra's directed graph Dreyfus efficient evaluator example expected number fifteen puzzle finding the shortest forward uni-directional method goal node Graph size 500 Graph Traverser gt(k hash heuristic function heuristic search INTEGER ARRAY intersection iteration lemma Manhattan distance monotonic decreasing Nicholson's graph nodes visited number of nodes number of steps OOO OOO OOO optimal path length placed in set predecessor procedure Proof puzzle configuration red amoeba rest q's search tree sequence Set B d(x set of nodes shortest path problem shortest path space solved spanning tree sparse graphs successors symmetric terminating condition theorem 4.3 VGAR VGHA wf(x wt(x