Minimum cut of directed planar graphs in O(n log log n) time

Shay Mozes; Kirill Nikolaev; Yahav Nussbaum; Oren Weimann

doi:10.1137/1.9781611975031.32

Minimum cut of directed planar graphs in O(n log log n) time

Shay Mozes
, Kirill Nikolaev
, Yahav Nussbaum
, Oren Weimann

Department of Computer Science

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

Abstract

We give an O(n log log n) time algorithm for computing the minimum cut (or equivalently, the shortest cycle) of a weighted directed planar graph. This improves the previous fastest O(n log3 n) solution. Interestingly, while in undirected planar graphs both min cut and min st-cut have O(n log log n) solutions, in directed planar graphs our result makes min cut faster than min st-cut, which currently requires O(n log n).

Original language	English
Title of host publication	29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
Editors	Artur Czumaj
Publisher	Association for Computing Machinery
Pages	477-494
Number of pages	18
ISBN (Electronic)	9781611975031
DOIs	https://doi.org/10.1137/1.9781611975031.32
State	Published - 2018
Event	29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 - New Orleans, United States Duration: 7 Jan 2018 → 10 Jan 2018

Publication series

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

Conference

Conference	29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
Country/Territory	United States
City	New Orleans
Period	7/01/18 → 10/01/18

Bibliographical note

Publisher Copyright:
© Copyright 2018 by SIAM.

ASJC Scopus subject areas

Software
General Mathematics

Access to Document

10.1137/1.9781611975031.32

Cite this

Mozes, S., Nikolaev, K., Nussbaum, Y., & Weimann, O. (2018). Minimum cut of directed planar graphs in O(n log log n) time. In A. Czumaj (Ed.), 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 (pp. 477-494). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery. https://doi.org/10.1137/1.9781611975031.32

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title = "Minimum cut of directed planar graphs in O(n log log n) time",

abstract = "We give an O(n log log n) time algorithm for computing the minimum cut (or equivalently, the shortest cycle) of a weighted directed planar graph. This improves the previous fastest O(n log3 n) solution. Interestingly, while in undirected planar graphs both min cut and min st-cut have O(n log log n) solutions, in directed planar graphs our result makes min cut faster than min st-cut, which currently requires O(n log n).",

author = "Shay Mozes and Kirill Nikolaev and Yahav Nussbaum and Oren Weimann",

year = "2018",

doi = "10.1137/1.9781611975031.32",

language = "English",

series = "Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms",

publisher = "Association for Computing Machinery",

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Mozes, S, Nikolaev, K, Nussbaum, Y & Weimann, O 2018, Minimum cut of directed planar graphs in O(n log log n) time. in A Czumaj (ed.), 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Association for Computing Machinery, pp. 477-494, 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018, New Orleans, United States, 7/01/18. https://doi.org/10.1137/1.9781611975031.32

Minimum cut of directed planar graphs in O(n log log n) time. / Mozes, Shay; Nikolaev, Kirill; Nussbaum, Yahav et al.
29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018. ed. / Artur Czumaj. Association for Computing Machinery, 2018. p. 477-494 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).

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

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AB - We give an O(n log log n) time algorithm for computing the minimum cut (or equivalently, the shortest cycle) of a weighted directed planar graph. This improves the previous fastest O(n log3 n) solution. Interestingly, while in undirected planar graphs both min cut and min st-cut have O(n log log n) solutions, in directed planar graphs our result makes min cut faster than min st-cut, which currently requires O(n log n).

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Minimum cut of directed planar graphs in O(n log log n) time

Abstract

Publication series

Conference

Bibliographical note

ASJC Scopus subject areas

Access to Document

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