Improved approximation guarantees through higher levels of SDP hierarchies

Eden Chlamtac; Gyanit Singh

doi:10.1007/978-3-540-85363-3_5

Improved approximation guarantees through higher levels of SDP hierarchies

Eden Chlamtac, Gyanit Singh

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

38 Scopus citations

Abstract

For every fixed γ ≥ 0, we give an algorithm that, given an n-vertex 3-uniform hypergraph containing an independent set of size γn, finds an independent set of size . This improves upon a recent result of Chlamtac, which, for a fixed ε > 0, finds an independent set of size n ^ε in any 3-uniform hypergraph containing an independent set of size . The main feature of this algorithm is that, for fixed γ, it uses the Θ(1/γ ²)-level of a hierarchy of semidefinite programming (SDP) relaxations. On the other hand, we show that for at least one hierarchy which gives such a guarantee, 1/γ levels yield no non-trivial guarantee. Thus, this is a first SDP-based algorithm for which the approximation guarantee improves indefinitely as one uses progressively higher-level relaxations.

Original language	English
Title of host publication	Approximation, Randomization and Combinatorial Optimization
Subtitle of host publication	Algorithms and Techniques - 11th International Workshop, APPROX 2008 and 12th International Workshop, RANDOM 2008, Proceedings
Pages	49-62
Number of pages	14
DOIs	https://doi.org/10.1007/978-3-540-85363-3_5
State	Published - 22 Sep 2008
Externally published	Yes
Event	11th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2008 and 12th International Workshop on Randomization and Computation, RANDOM 2008 - Boston, MA, United States Duration: 25 Aug 2008 → 27 Aug 2008

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5171 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	11th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2008 and 12th International Workshop on Randomization and Computation, RANDOM 2008
Country/Territory	United States
City	Boston, MA
Period	25/08/08 → 27/08/08

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-540-85363-3_5

Cite this

Chlamtac, E., & Singh, G. (2008). Improved approximation guarantees through higher levels of SDP hierarchies. In Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques - 11th International Workshop, APPROX 2008 and 12th International Workshop, RANDOM 2008, Proceedings (pp. 49-62). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5171 LNCS). https://doi.org/10.1007/978-3-540-85363-3_5

Chlamtac, Eden ; Singh, Gyanit. / Improved approximation guarantees through higher levels of SDP hierarchies. Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques - 11th International Workshop, APPROX 2008 and 12th International Workshop, RANDOM 2008, Proceedings. 2008. pp. 49-62 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Chlamtac, E & Singh, G 2008, Improved approximation guarantees through higher levels of SDP hierarchies. in Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques - 11th International Workshop, APPROX 2008 and 12th International Workshop, RANDOM 2008, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5171 LNCS, pp. 49-62, 11th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2008 and 12th International Workshop on Randomization and Computation, RANDOM 2008, Boston, MA, United States, 25/08/08. https://doi.org/10.1007/978-3-540-85363-3_5

Improved approximation guarantees through higher levels of SDP hierarchies. / Chlamtac, Eden; Singh, Gyanit.
Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques - 11th International Workshop, APPROX 2008 and 12th International Workshop, RANDOM 2008, Proceedings. 2008. p. 49-62 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5171 LNCS).

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

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Chlamtac E, Singh G. Improved approximation guarantees through higher levels of SDP hierarchies. In Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques - 11th International Workshop, APPROX 2008 and 12th International Workshop, RANDOM 2008, Proceedings. 2008. p. 49-62. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-85363-3_5

Improved approximation guarantees through higher levels of SDP hierarchies

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