TY - GEN

T1 - Computing replacement paths in surface embedded graphs

AU - Erickson, Jeff

AU - Nayyeri, Amir

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2011

Y1 - 2011

N2 - 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].

AB - 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].

UR - http://www.scopus.com/inward/record.url?scp=79955745818&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955745818&partnerID=8YFLogxK

U2 - 10.1137/1.9781611973082.103

DO - 10.1137/1.9781611973082.103

M3 - Conference contribution

AN - SCOPUS:79955745818

SN - 9780898719932

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1347

EP - 1354

BT - Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011

PB - Association for Computing Machinery

ER -