Efficient algorithms for path problems with general cost criteria

Abstract

Recent applications of path problems in engineering, e.g., in circuit design require the computation of optimal paths with respect to general cost criteria going beyond path length. In this paper we extend the path algorithms by Ford and Dijkstra to handle a wide variety of cost criteria which can be nonassociative, nonmonotonic, partially ordered, and not antisymmetric. Negative cycles are allowed, so our search method is more powerful than best-first search. In addition we analyze the efficiency of the presented algorithms. The method gives efficient algorithms for a number of applications. We give several examples. Among them are finding paths with minimum frequency of the most frequent edge cost and finding paths with minimum range in edge cost. Finally, we describe goal-directed versions of our search methods.