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A Quadratic Algorithm for Finding Next-to-Shortest Paths in Graphs

Authors:

Kuo-Hua Kao,

Jou-Ming Chang,

Yue-Li Wang,

Justie Su-Tzu JuanAuthors Info & Claims

Algorithmica, Volume 61, Issue 2

Pages 402 - 418

https://doi.org/10.1007/s00453-010-9402-4

Published: 01 October 2011 Publication History

Abstract

Given an edge-weighted undirected graph G and two prescribed vertices u and v, a next-to-shortest (u,v)-path is a shortest (u,v)-path amongst all (u,v)-paths having length strictly greater than the length of a shortest (u,v)-path. In this paper, we deal with the problem of computing a next-to-shortest (u,v)-path. We propose an ${\mathcal{O}}(n^{2})$ time algorithm for solving this problem, which significantly improves the bound of a previous one in ${\mathcal{O}}(n^{3})$ time where n is the number of vertices in G.

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Demaine EHuang YLiao CSadakane K(2021)Approximating the Canadian Traveller Problem with Online RandomizationAlgorithmica10.1007/s00453-020-00792-683:5(1524-1543)Online publication date: 1-May-2021
https://dl.acm.org/doi/10.1007/s00453-020-00792-6
Wang XFan JJia XLin C(2016)An efficient algorithm to construct disjoint path covers of DCell networksTheoretical Computer Science10.1016/j.tcs.2015.09.022609:P1(197-210)Online publication date: 4-Jan-2016
https://dl.acm.org/doi/10.1016/j.tcs.2015.09.022
Wu BWang H(2015)The next-to-shortest path problem on directed graphs with positive edge weightsNetworks10.1002/net.2159865:3(205-211)Online publication date: 1-May-2015
https://dl.acm.org/doi/10.1002/net.21598
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A Quadratic Algorithm for Finding Next-to-Shortest Paths in Graphs
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory

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Published In

Algorithmica Volume 61, Issue 2

October 2011

279 pages

ISSN:0178-4617

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 October 2011

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Demaine EHuang YLiao CSadakane K(2021)Approximating the Canadian Traveller Problem with Online RandomizationAlgorithmica10.1007/s00453-020-00792-683:5(1524-1543)Online publication date: 1-May-2021
https://dl.acm.org/doi/10.1007/s00453-020-00792-6
Wang XFan JJia XLin C(2016)An efficient algorithm to construct disjoint path covers of DCell networksTheoretical Computer Science10.1016/j.tcs.2015.09.022609:P1(197-210)Online publication date: 4-Jan-2016
https://dl.acm.org/doi/10.1016/j.tcs.2015.09.022
Wu BWang H(2015)The next-to-shortest path problem on directed graphs with positive edge weightsNetworks10.1002/net.2159865:3(205-211)Online publication date: 1-May-2015
https://dl.acm.org/doi/10.1002/net.21598
Wu B(2013)A Simpler and More Efficient Algorithm for the Next-to-Shortest Path ProblemAlgorithmica10.1007/s00453-011-9601-765:2(467-479)Online publication date: 1-Feb-2013
https://dl.acm.org/doi/10.1007/s00453-011-9601-7
Zhang LYan YZhao SZhang Y(2013)Network Performance Analysis Based on Quotient Space TheoryProceedings of the 14th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing - Volume 817010.1007/978-3-642-41218-9_23(216-224)Online publication date: 11-Oct-2013
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Zhang CNagamochi H(2012)The next-to-shortest path in undirected graphs with nonnegative weightsProceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 12810.5555/2523693.2523695(13-20)Online publication date: 31-Jan-2012
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Wu B(2010)A simpler and more efficient algorithm for the next-to-shortest path problemProceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II10.5555/1940424.1940442(219-227)Online publication date: 18-Dec-2010
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