Solving the replacement paths problem for planar directed graphs in O(n logn) time

Christian Wulff-Nilsen

doi:10.1137/1.9781611973075.62

Solving the replacement paths problem for planar directed graphs in O(n logn) time

Department of Computer Science

Abstract

In a graph G with non-negative edge lengths, let P be a shortest path from a vertex s to a vertex t. We consider the problem of computing, for each edge e on P, the length of a shortest path in G from s to t that avoids e. This is known as the replacement paths problem. We give a linearspace algorithm with O(n log n) running time for n-vertex planar directed graphs. The previous best time bound was O(n log2 n).

Original language	English
Title of host publication	Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms
Editors	Moses Charikar
Number of pages	10
Publisher	Society for Industrial and Applied Mathematics
Publication date	2010
Pages	756-765
ISBN (Print)	978-0-89871-701-3
ISBN (Electronic)	978-1-61197-307-5
DOIs	https://doi.org/10.1137/1.9781611973075.62
Publication status	Published - 2010
Event	21st Annual ACM-SIAM Symposium on Discrete Algorithms - Austin, United States Duration: 17 Jan 2010 → 19 Jan 2010 Conference number: 21

Conference

Conference	21st Annual ACM-SIAM Symposium on Discrete Algorithms
Number	21
Country/Territory	United States
City	Austin
Period	17/01/2010 → 19/01/2010

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10.1137/1.9781611973075.62

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Solving the replacement paths problem for planar directed graphs in O(n logn) time. / Wulff-Nilsen, Christian.
Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms. ed. / Moses Charikar. Society for Industrial and Applied Mathematics, 2010. p. 756-765.

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Wulff-Nilsen, C 2010, Solving the replacement paths problem for planar directed graphs in O(n logn) time. in M Charikar (ed.), Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics, pp. 756-765, 21st Annual ACM-SIAM Symposium on Discrete Algorithms, Austin, United States, 17/01/2010. https://doi.org/10.1137/1.9781611973075.62

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abstract = "In a graph G with non-negative edge lengths, let P be a shortest path from a vertex s to a vertex t. We consider the problem of computing, for each edge e on P, the length of a shortest path in G from s to t that avoids e. This is known as the replacement paths problem. We give a linearspace algorithm with O(n log n) running time for n-vertex planar directed graphs. The previous best time bound was O(n log2 n).",

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Y2 - 17 January 2010 through 19 January 2010

ER -

Solving the replacement paths problem for planar directed graphs in O(n logn) time

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