Enumerating K best paths in length order in DAGs

Marta M.B. Pascoal and Antonio Sedeño-Noda

European Journal of Operational Research, 2012, vol. 221, issue 2, 308-316

Abstract: We address the problem of finding the K best paths connecting a given pair of nodes in a directed acyclic graph (DAG) with arbitrary lengths. One of the main results in this paper is the proof that a tree representing the kth shortest path is obtained by an arc exchange in one of the previous (k−1) trees (each of which contains a previous best path). An O(m+K(n+logK)) time and O(K+m) space algorithm is designed to explicitly determine the K shortest paths in a DAG with n nodes and m arcs. The algorithm runs in O(m+Kn) time using O(K+m) space in DAGs with integer length arcs. Empirical results confirming the superior performance of the algorithm to others found in the literature for randomly generated graphs are reported.

Keywords: Combinatorial optimization; Shortest path algorithms; K best solutions (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:221:y:2012:i:2:p:308-316

DOI: 10.1016/j.ejor.2012.04.001

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