MAX CUT in cubic graphs

Eran Halperin; Dror Livnat; Uri Zwick

doi:10.1016/j.jalgor.2004.06.001

MAX CUT in cubic graphs

Eran Halperin, Dror Livnat, Uri Zwick^*

^*Corresponding author for this work

University of California at Berkeley

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

We present an improved semidefinite programming based approximation algorithm for the MAX CUT problem in graphs of maximum degree at most 3. The approximation ratio of the new algorithm is at least 0.9326. This improves, and also somewhat simplifies, a result of Feige, Karpinski and Langberg. We also observe that results of Hopkins and Staton and of Bondy and Locke yield a simple combinatorial 4/5-approximation algorithm for the problem. Finally, we present a combinatorial 22/27-approximation algorithm for the MAX CUT problem for regular cubic graphs.

Original language	English
Pages (from-to)	169-185
Number of pages	17
Journal	Journal of Algorithms
Volume	53
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgor.2004.06.001
State	Published - Nov 2004

Funding

Funders	Funder number
Israel Science Foundation	246/01

Access to Document

10.1016/j.jalgor.2004.06.001

Cite this

@article{3e583748f35c429fa7f30f7b5aa9c6c9,

title = "MAX CUT in cubic graphs",

abstract = "We present an improved semidefinite programming based approximation algorithm for the MAX CUT problem in graphs of maximum degree at most 3. The approximation ratio of the new algorithm is at least 0.9326. This improves, and also somewhat simplifies, a result of Feige, Karpinski and Langberg. We also observe that results of Hopkins and Staton and of Bondy and Locke yield a simple combinatorial 4/5-approximation algorithm for the problem. Finally, we present a combinatorial 22/27-approximation algorithm for the MAX CUT problem for regular cubic graphs.",

author = "Eran Halperin and Dror Livnat and Uri Zwick",

note = "Funding Information: ✩ This research was supported by the Israel Science Foundation (grant no. 246/01). A preliminary version of this paper appeared in [E. Halperin, D. Livnat, U. Zwick, MAX CUT in cubic graphs, in: Proceedings of the 13th Annual ACM–SIAM Symposium on Discrete Algorithms, San Francisco, CA, 2002, pp. 506–513]. * Corresponding author. E-mail addresses: [email protected] (E. Halperin), [email protected] (D. Livnat), [email protected] (U. Zwick).",

year = "2004",

month = nov,

doi = "10.1016/j.jalgor.2004.06.001",

language = "אנגלית",

volume = "53",

pages = "169--185",

journal = "Journal of Algorithms",

issn = "0196-6774",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - MAX CUT in cubic graphs

AU - Halperin, Eran

AU - Livnat, Dror

AU - Zwick, Uri

N1 - Funding Information: ✩ This research was supported by the Israel Science Foundation (grant no. 246/01). A preliminary version of this paper appeared in [E. Halperin, D. Livnat, U. Zwick, MAX CUT in cubic graphs, in: Proceedings of the 13th Annual ACM–SIAM Symposium on Discrete Algorithms, San Francisco, CA, 2002, pp. 506–513]. * Corresponding author. E-mail addresses: [email protected] (E. Halperin), [email protected] (D. Livnat), [email protected] (U. Zwick).

PY - 2004/11

Y1 - 2004/11

N2 - We present an improved semidefinite programming based approximation algorithm for the MAX CUT problem in graphs of maximum degree at most 3. The approximation ratio of the new algorithm is at least 0.9326. This improves, and also somewhat simplifies, a result of Feige, Karpinski and Langberg. We also observe that results of Hopkins and Staton and of Bondy and Locke yield a simple combinatorial 4/5-approximation algorithm for the problem. Finally, we present a combinatorial 22/27-approximation algorithm for the MAX CUT problem for regular cubic graphs.

AB - We present an improved semidefinite programming based approximation algorithm for the MAX CUT problem in graphs of maximum degree at most 3. The approximation ratio of the new algorithm is at least 0.9326. This improves, and also somewhat simplifies, a result of Feige, Karpinski and Langberg. We also observe that results of Hopkins and Staton and of Bondy and Locke yield a simple combinatorial 4/5-approximation algorithm for the problem. Finally, we present a combinatorial 22/27-approximation algorithm for the MAX CUT problem for regular cubic graphs.

UR - http://www.scopus.com/inward/record.url?scp=3943069695&partnerID=8YFLogxK

U2 - 10.1016/j.jalgor.2004.06.001

DO - 10.1016/j.jalgor.2004.06.001

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:3943069695

SN - 0196-6774

VL - 53

SP - 169

EP - 185

JO - Journal of Algorithms

JF - Journal of Algorithms

IS - 2

ER -

MAX CUT in cubic graphs

Abstract

Funding

Access to Document

Other files and links

Fingerprint

Cite this