Inapproximability of vertex cover and independent set in bounded degree graphs

Per Austrin, Subhash Khot, Muli Safra

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study the inapproximability of Vertex Cover and Independent Set on degree d graphs. We prove that: • Vertex Cover is Unique Games-hard to approximate to within a factor 2-(2+od(1))/log log d/log d . This exactly matches the algorithmic result of Halperin [1] up to the o d(1) term. • Independent Set is Unique Games-hard to approximate to within a factor O/( d/log2 d ). This improves the d/log O(1)(d) Unique Games hardness result of Samorodnitsky and Trevisan [2]. Additionally, our result does not rely on the construction of a query efficient PCP as in [2].

Original languageEnglish (US)
Title of host publicationProceedings of the 2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009
Pages74-80
Number of pages7
DOIs
StatePublished - 2009
Event2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009 - Paris, France
Duration: Jul 15 2009Jul 18 2009

Other

Other2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009
CountryFrance
CityParis
Period7/15/097/18/09

Fingerprint

Inapproximability
Vertex Cover
Independent Set
Hardness
Game
Graph in graph theory
Query
Term

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Computational Mathematics

Cite this

Austrin, P., Khot, S., & Safra, M. (2009). Inapproximability of vertex cover and independent set in bounded degree graphs. In Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009 (pp. 74-80). [5231231] https://doi.org/10.1109/CCC.2009.38

Inapproximability of vertex cover and independent set in bounded degree graphs. / Austrin, Per; Khot, Subhash; Safra, Muli.

Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009. 2009. p. 74-80 5231231.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Austrin, P, Khot, S & Safra, M 2009, Inapproximability of vertex cover and independent set in bounded degree graphs. in Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009., 5231231, pp. 74-80, 2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009, Paris, France, 7/15/09. https://doi.org/10.1109/CCC.2009.38
Austrin P, Khot S, Safra M. Inapproximability of vertex cover and independent set in bounded degree graphs. In Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009. 2009. p. 74-80. 5231231 https://doi.org/10.1109/CCC.2009.38
Austrin, Per ; Khot, Subhash ; Safra, Muli. / Inapproximability of vertex cover and independent set in bounded degree graphs. Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009. 2009. pp. 74-80
@inproceedings{1729f8510a794bffb7218d381953603c,
title = "Inapproximability of vertex cover and independent set in bounded degree graphs",
abstract = "We study the inapproximability of Vertex Cover and Independent Set on degree d graphs. We prove that: • Vertex Cover is Unique Games-hard to approximate to within a factor 2-(2+od(1))/log log d/log d . This exactly matches the algorithmic result of Halperin [1] up to the o d(1) term. • Independent Set is Unique Games-hard to approximate to within a factor O/( d/log2 d ). This improves the d/log O(1)(d) Unique Games hardness result of Samorodnitsky and Trevisan [2]. Additionally, our result does not rely on the construction of a query efficient PCP as in [2].",
author = "Per Austrin and Subhash Khot and Muli Safra",
year = "2009",
doi = "10.1109/CCC.2009.38",
language = "English (US)",
isbn = "9780769537177",
pages = "74--80",
booktitle = "Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009",

}

TY - GEN

T1 - Inapproximability of vertex cover and independent set in bounded degree graphs

AU - Austrin, Per

AU - Khot, Subhash

AU - Safra, Muli

PY - 2009

Y1 - 2009

N2 - We study the inapproximability of Vertex Cover and Independent Set on degree d graphs. We prove that: • Vertex Cover is Unique Games-hard to approximate to within a factor 2-(2+od(1))/log log d/log d . This exactly matches the algorithmic result of Halperin [1] up to the o d(1) term. • Independent Set is Unique Games-hard to approximate to within a factor O/( d/log2 d ). This improves the d/log O(1)(d) Unique Games hardness result of Samorodnitsky and Trevisan [2]. Additionally, our result does not rely on the construction of a query efficient PCP as in [2].

AB - We study the inapproximability of Vertex Cover and Independent Set on degree d graphs. We prove that: • Vertex Cover is Unique Games-hard to approximate to within a factor 2-(2+od(1))/log log d/log d . This exactly matches the algorithmic result of Halperin [1] up to the o d(1) term. • Independent Set is Unique Games-hard to approximate to within a factor O/( d/log2 d ). This improves the d/log O(1)(d) Unique Games hardness result of Samorodnitsky and Trevisan [2]. Additionally, our result does not rely on the construction of a query efficient PCP as in [2].

UR - http://www.scopus.com/inward/record.url?scp=70350626961&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350626961&partnerID=8YFLogxK

U2 - 10.1109/CCC.2009.38

DO - 10.1109/CCC.2009.38

M3 - Conference contribution

SN - 9780769537177

SP - 74

EP - 80

BT - Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009

ER -