Computing replacement paths in surface-embedded graphs

Written with Amir Nayyeri*

Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, 1347–1354, 2011.

Let s and t be vertices in a directed graph G with non-negative edge weights. The replacement paths problem asks us to compute, for each edge e in G, the length of the shortest path from s to t that does not traverse e. We describe an algorithm that solves the replacement paths problem for directed graphs embedded on a surface of any genus g in O(gn log n) time, generalizing a recent O(n log n)-time algorithm of Wulff-Nilsen for planar graphs [SODA 2010].

Publications - Jeff Erickson ( 21 Jan 2012