On the complexity of admissible search algorithms

This paper analyzes the complexity of heuristic search algorithms, i.e. algorithms which find the shortest path in a graph by using an estimate to guide the search. In particular, algorithm A¹, due to Hart, Nilsson and Raphael, is shown to require O(2^N) steps, in the worst case, for searching a graph with N nodes, if the so called “consistency assumption” does not hold for the estimate. Furthermore, a new search algorithm is presented which runs in O(N²) steps in the worst case and which never requires more steps than A¹.