Approximation algorithm for sparsest k-partitioning

Anand Louis; Konstantin Makarychev

doi:10.1137/1.9781611973402.92

Approximation algorithm for sparsest k-partitioning

Anand Louis^*, Konstantin Makarychev

^*Corresponding author for this work

Computer Science

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

12 Scopus citations

Abstract

Given a graph G, the sparsest-cut problem asks to find the set of vertices S which has the least expansion defined as , φ_G(S) =def w(E(S,S̄)) /min{w(S), w(S̄)} where w is the total edge weight of a subset. Here we study the natural generalization of this problem: given an integer k, compute a k-partition {P₁...., P_k} of the vertex set so as to minimize φ^k_G({P ₁,...,P_k})=def max I φ_G(P_i). Our main result is a polynomial time bi-criteria approximation algorithm which outputs a (1 - ε)k-partition of the vertex set such that each piece has expansion at most O_ε (√log n log k) times OPT. We also study balanced versions of this problem.

Original language	English (US)
Title of host publication	Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014
Publisher	Association for Computing Machinery
Pages	1244-1255
Number of pages	12
ISBN (Print)	9781611973389
DOIs	https://doi.org/10.1137/1.9781611973402.92
State	Published - 2014
Event	25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014 - Portland, OR, United States Duration: Jan 5 2014 → Jan 7 2014

Publication series

Name	Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Other

Other	25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014
Country	United States
City	Portland, OR
Period	1/5/14 → 1/7/14

ASJC Scopus subject areas

Software
Mathematics(all)

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10.1137/1.9781611973402.92

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title = "Approximation algorithm for sparsest k-partitioning",

abstract = "Given a graph G, the sparsest-cut problem asks to find the set of vertices S which has the least expansion defined as , φG(S) =def w(E(S,{\=S})) /min{w(S), w({\=S})} where w is the total edge weight of a subset. Here we study the natural generalization of this problem: given an integer k, compute a k-partition {P1...., Pk} of the vertex set so as to minimize φkG({P 1,...,Pk})=def max I φG(Pi). Our main result is a polynomial time bi-criteria approximation algorithm which outputs a (1 - ε)k-partition of the vertex set such that each piece has expansion at most Oε (√log n log k) times OPT. We also study balanced versions of this problem.",

author = "Anand Louis and Konstantin Makarychev",

year = "2014",

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language = "English (US)",

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

publisher = "Association for Computing Machinery",

pages = "1244--1255",

booktitle = "Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014",

note = "25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014 ; Conference date: 05-01-2014 Through 07-01-2014",

}

Louis, A & Makarychev, K 2014, Approximation algorithm for sparsest k-partitioning. in Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Association for Computing Machinery, pp. 1244-1255, 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014, Portland, OR, United States, 1/5/14. https://doi.org/10.1137/1.9781611973402.92

Approximation algorithm for sparsest k-partitioning. / Louis, Anand; Makarychev, Konstantin.

Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014. Association for Computing Machinery, 2014. p. 1244-1255 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms).

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

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N2 - Given a graph G, the sparsest-cut problem asks to find the set of vertices S which has the least expansion defined as , φG(S) =def w(E(S,S̄)) /min{w(S), w(S̄)} where w is the total edge weight of a subset. Here we study the natural generalization of this problem: given an integer k, compute a k-partition {P1...., Pk} of the vertex set so as to minimize φkG({P 1,...,Pk})=def max I φG(Pi). Our main result is a polynomial time bi-criteria approximation algorithm which outputs a (1 - ε)k-partition of the vertex set such that each piece has expansion at most Oε (√log n log k) times OPT. We also study balanced versions of this problem.

AB - Given a graph G, the sparsest-cut problem asks to find the set of vertices S which has the least expansion defined as , φG(S) =def w(E(S,S̄)) /min{w(S), w(S̄)} where w is the total edge weight of a subset. Here we study the natural generalization of this problem: given an integer k, compute a k-partition {P1...., Pk} of the vertex set so as to minimize φkG({P 1,...,Pk})=def max I φG(Pi). Our main result is a polynomial time bi-criteria approximation algorithm which outputs a (1 - ε)k-partition of the vertex set such that each piece has expansion at most Oε (√log n log k) times OPT. We also study balanced versions of this problem.

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Approximation algorithm for sparsest k-partitioning

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