O(√log n) approximation algorithms for Min UnCut, Min 2CNF Deletion, and Directed Cut problems

Amit Agarwal; Konstantin Makarychev; Moses Charikar; Yury Makarychev

doi:10.1145/1060590.1060675

O(√log n) approximation algorithms for Min UnCut, Min 2CNF Deletion, and Directed Cut problems

Amit Agarwal^*, Konstantin Makarychev, Moses Charikar, Yury Makarychev

^*Corresponding author for this work

Computer Science

Research output: Contribution to journal › Conference article › peer-review

112 Scopus citations

Abstract

We give O(√log n)-approxiniation algorithms for the MIN UNCUT, MIN 2CNF DELETION, DIRECTED BALANCED SEPARATOR, and DIRECTED SPARSEST CUT problems. The previously best known algorithms give an O(log n)-approximation for MIN UNCUT [9], DIRECTED BALANCED SEPARATOR [17], DIRECTED SPARSEST CUT [17], and an O(log n log log n)-approximation for MIN 2CNF DELETION [14]. We also show that the integrality gap of an SDP relaxation of the MINIMUM MULTICUT problem is Ω(log n).

Original language	English (US)
Pages (from-to)	573-581
Number of pages	9
Journal	Proceedings of the Annual ACM Symposium on Theory of Computing
DOIs	https://doi.org/10.1145/1060590.1060675
State	Published - Dec 1 2005
Event	13th Color Imaging Conference: Color Science, Systems, Technologies, and Applications - Scottsdale, AZ, United States Duration: Nov 7 2005 → Nov 11 2005

Keywords

Directed Balanced Separator
Directed Sparsest Cut
Min 2CNF Deletion
Min Multicut
Min UnCut

ASJC Scopus subject areas

Software

Access to Document

10.1145/1060590.1060675

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title = "O(√log n) approximation algorithms for Min UnCut, Min 2CNF Deletion, and Directed Cut problems",

abstract = "We give O(√log n)-approxiniation algorithms for the MIN UNCUT, MIN 2CNF DELETION, DIRECTED BALANCED SEPARATOR, and DIRECTED SPARSEST CUT problems. The previously best known algorithms give an O(log n)-approximation for MIN UNCUT [9], DIRECTED BALANCED SEPARATOR [17], DIRECTED SPARSEST CUT [17], and an O(log n log log n)-approximation for MIN 2CNF DELETION [14]. We also show that the integrality gap of an SDP relaxation of the MINIMUM MULTICUT problem is Ω(log n).",

keywords = "Directed Balanced Separator, Directed Sparsest Cut, Min 2CNF Deletion, Min Multicut, Min UnCut",

author = "Amit Agarwal and Konstantin Makarychev and Moses Charikar and Yury Makarychev",

year = "2005",

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language = "English (US)",

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AU - Makarychev, Yury

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AB - We give O(√log n)-approxiniation algorithms for the MIN UNCUT, MIN 2CNF DELETION, DIRECTED BALANCED SEPARATOR, and DIRECTED SPARSEST CUT problems. The previously best known algorithms give an O(log n)-approximation for MIN UNCUT [9], DIRECTED BALANCED SEPARATOR [17], DIRECTED SPARSEST CUT [17], and an O(log n log log n)-approximation for MIN 2CNF DELETION [14]. We also show that the integrality gap of an SDP relaxation of the MINIMUM MULTICUT problem is Ω(log n).

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