Single source shortest paths in H-minor free graphs

Authors:
Raphael Yuster
Affiliations:
Department of Mathematics, University of Haifa, Haifa 31905, Israel
Venue:
Theoretical Computer Science
Year:
2010

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Abstract

We present an algorithm for the Single Source Shortest Paths (SSSP) problem in directedH-minor free graphs. For every fixed H, if G is a graph with n vertices having integer edge lengths and s is a designated source vertex of G, the algorithm runs in O@?(n^1^1^.^5^-^2logL)@?O(n^1^.^3^9^2logL) time, where L is the absolute value of the smallest edge length. The algorithm computes the shortest paths and the distances from s to all vertices of the graph, or else provides a certificate that G is not H-minor free. Our result improves an earlier O(n^1^.^5logL) time algorithm for this problem, which follows from a general SSSP algorithm of Goldberg.