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**1 - 1**of**1**### Computing Replacement Paths in Surface Embedded Graphs

, 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 ..."

Abstract
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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].