Finding the k shortest paths

  • Authors:
  • D. Eppstein

  • Affiliations:
  • Dept. of Inf.&Comput. Sci., California Univ., Irvine, CA, USA

  • Venue:
  • SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
  • Year:
  • 1994

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Abstract

We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m+n log n+k). We can also find the k shortest paths from a given source s to each vertex in the graph, in total time O(m+n log n+kn). We describe applications to dynamic programming problems including the knapsack problem, sequence alignment, and maximum inscribed polygons.