A 4 + ε approximation for k-connected subgraphs

Zeev Nutov

doi:10.1137/1.9781611975994.60

A 4 + ε approximation for k-connected subgraphs

Zeev Nutov

Computer Science

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

Abstract

We obtain approximation ratio (equation presented) for the (undirected) k-Connected Subgraph problem, where l = (equation presented) is the largest integer such that 2^l−¹k^2l⁺¹ ≤ n. For large values of n this improves the ratio 6 of Cheriyan and Végh [4] when n ≥ k³ (the case l = 1). Our result implies an fpt-approximation ratio 4 + ε that matches (up to the “+ε” term) the best known ratio 4 for k = 6, 7 for both the general and the easier augmentation versions of the problem. Similar results are shown for the problem of covering an arbitrary crossing supermodular biset function.

Original language	English
Title of host publication	31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020
Editors	Shuchi Chawla
Publisher	Association for Computing Machinery
Pages	1000-1009
Number of pages	10
ISBN (Electronic)	9781611975994
DOIs	https://doi.org/10.1137/1.9781611975994.60
State	Published - 2020
Event	31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020 - Salt Lake City, United States Duration: 5 Jan 2020 → 8 Jan 2020

Publication series

Name	Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume	2020-January
ISSN (Print)	1071-9040
ISSN (Electronic)	1557-9468

Conference

Conference	31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020
Country/Territory	United States
City	Salt Lake City
Period	5/01/20 → 8/01/20

Bibliographical note

Publisher Copyright:
Copyright © 2020 by SIAM

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10.1137/1.9781611975994.60

Cite this

@inproceedings{a7a6794485ce4405822071612b4a7f07,

title = "A 4 + ε approximation for k-connected subgraphs",

abstract = "We obtain approximation ratio (equation presented) for the (undirected) k-Connected Subgraph problem, where l = (equation presented) is the largest integer such that 2l−1k2l+1 ≤ n. For large values of n this improves the ratio 6 of Cheriyan and V{\'e}gh [4] when n ≥ k3 (the case l = 1). Our result implies an fpt-approximation ratio 4 + ε that matches (up to the “+ε” term) the best known ratio 4 for k = 6, 7 for both the general and the easier augmentation versions of the problem. Similar results are shown for the problem of covering an arbitrary crossing supermodular biset function.",

author = "Zeev Nutov",

note = "Publisher Copyright: Copyright {\textcopyright} 2020 by SIAM Copyright: Copyright 2020 Elsevier B.V., All rights reserved.; 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020 ; Conference date: 05-01-2020 Through 08-01-2020",

year = "2020",

doi = "10.1137/1.9781611975994.60",

language = "אנגלית",

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

publisher = "Association for Computing Machinery",

pages = "1000--1009",

editor = "Shuchi Chawla",

booktitle = "31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020",

}

Nutov, Z 2020, A 4 + ε approximation for k-connected subgraphs. in S Chawla (ed.), 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 2020-January, Association for Computing Machinery, pp. 1000-1009, 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020, Salt Lake City, United States, 5/01/20. https://doi.org/10.1137/1.9781611975994.60

A 4 + ε approximation for k-connected subgraphs. / Nutov, Zeev.
31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020. ed. / Shuchi Chawla. Association for Computing Machinery, 2020. p. 1000-1009 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 2020-January).

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

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AB - We obtain approximation ratio (equation presented) for the (undirected) k-Connected Subgraph problem, where l = (equation presented) is the largest integer such that 2l−1k2l+1 ≤ n. For large values of n this improves the ratio 6 of Cheriyan and Végh [4] when n ≥ k3 (the case l = 1). Our result implies an fpt-approximation ratio 4 + ε that matches (up to the “+ε” term) the best known ratio 4 for k = 6, 7 for both the general and the easier augmentation versions of the problem. Similar results are shown for the problem of covering an arbitrary crossing supermodular biset function.

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A 4 + ε approximation for k-connected subgraphs

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