Near-optimal approximation algorithm for simultaneous Max-cut

Amey Bhangale, Subhash Khot, Swastik Kopparty, Sushant Sachdeva, Devanathan Thiruvenkatachari

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

Abstract

In the simultaneous Max-Cut problem, we are given k weighted graphs on the same set of n vertices, and the goal is to find a cut of the vertex set so that the minimum, over the k graphs, of the cut value is as large as possible. Previous work [BKS15] gave a polynomial time algorithm which achieved an approximation factor of 1-2- op1q for this problem (and an approximation factor of 1-2 + ϵk in the unweighted case, where "k Ñ 0 as k Ñ 8). In this work, we give a polynomial time approximation algorithm for simultaneous Max-Cut with an approximation factor of 0:8780 (for all constant k). The natural SDP formulation for simultaneous Max-Cut was shown to have an integrality gap of 1-2+ϵk in [BKS15]. In achieving the better approximation guarantee, we use a stronger Sum-of-Squares hierarchy SDP relaxation and a rounding algorithm based on Raghavendra-Tan [RT12], in addition to techniques from [BKS15].

Original languageEnglish (US)
Title of host publication29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
PublisherAssociation for Computing Machinery
Pages1407-1425
Number of pages19
ISBN (Electronic)9781611975031
DOIs
StatePublished - Jan 1 2018
Event29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 - New Orleans, United States
Duration: Jan 7 2018Jan 10 2018

Other

Other29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
CountryUnited States
CityNew Orleans
Period1/7/181/10/18

Fingerprint

Max-cut
Optimal Approximation
Approximation algorithms
Optimal Algorithm
Approximation Algorithms
Polynomials
Approximation
Polynomial-time Algorithm
Max-cut Problem
Integrality
Rounding
Sum of squares
Weighted Graph
Formulation
Graph in graph theory
Vertex of a graph

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

Cite this

Bhangale, A., Khot, S., Kopparty, S., Sachdeva, S., & Thiruvenkatachari, D. (2018). Near-optimal approximation algorithm for simultaneous Max-cut. In 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 (pp. 1407-1425). Association for Computing Machinery. https://doi.org/10.1137/1.9781611975031.93

Near-optimal approximation algorithm for simultaneous Max-cut. / Bhangale, Amey; Khot, Subhash; Kopparty, Swastik; Sachdeva, Sushant; Thiruvenkatachari, Devanathan.

29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018. Association for Computing Machinery, 2018. p. 1407-1425.

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

Bhangale, A, Khot, S, Kopparty, S, Sachdeva, S & Thiruvenkatachari, D 2018, Near-optimal approximation algorithm for simultaneous Max-cut. in 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018. Association for Computing Machinery, pp. 1407-1425, 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018, New Orleans, United States, 1/7/18. https://doi.org/10.1137/1.9781611975031.93
Bhangale A, Khot S, Kopparty S, Sachdeva S, Thiruvenkatachari D. Near-optimal approximation algorithm for simultaneous Max-cut. In 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018. Association for Computing Machinery. 2018. p. 1407-1425 https://doi.org/10.1137/1.9781611975031.93
Bhangale, Amey ; Khot, Subhash ; Kopparty, Swastik ; Sachdeva, Sushant ; Thiruvenkatachari, Devanathan. / Near-optimal approximation algorithm for simultaneous Max-cut. 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018. Association for Computing Machinery, 2018. pp. 1407-1425
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