Chapter 2 - Basic Search Algorithms

Abstract

This chapter establishes that besides breadth- and depth-first search the (single-source shortest paths) algorithm of Dijkstra is of particular interest, since the heuristic search algorithm A* is a generalization of it. For nonconsistent heuristics, already explored nodes are reopened to preserve the optimality of the first solution. To compute the shortest (cheapest) path in graphs with nonnegative weights, Dijkstra proposed a greedy search strategy based on the principle of optimality . The difference of A* from all preceding algorithms is that it performs a heuristic search . A heuristic can improve search efficiency by providing an estimate of the remaining yet unexplored distance to a goal. Neither depth-first nor breadth-first search nor Dijkstra's algorithm takes advantage of such an estimate and is therefore also called uninformed search algorithms. This chapter proves the correctness of the approaches and discusses the optimal efficiency of A*.