A result on the computational complexity of heuristic estimates for the A* algorithm

The performance of a new heuristic search algorithm is analyzed in this paper. The algorithm uses a formal representation (semantic representation) that contains enough information to compute the heuristic evaluation function h(n), as defined in the context of A*, without requiring a human expert to provide it. The heuristic is computed by solving less constrained subproblems (auxiliary problems) of the given problem. The new algorithm is shown to be less efficient than the Dijkstra algorithm, according to the complexity measure "number of node expansions. " This proves that it is not efficient to compute heuristics for A * by solving auxiliary problems with backtracking. Basic Definitions and Auxiliary Problem