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Title: Combinatorial approximation algorithms for MAXCUT using random walks.

Abstract

We give the first combinatorial approximation algorithm for MaxCut that beats the trivial 0.5 factor by a constant. The main partitioning procedure is very intuitive, natural, and easily described. It essentially performs a number of random walks and aggregates the information to provide the partition. We can control the running time to get an approximation factor-running time tradeoff. We show that for any constant b > 1.5, there is an {tilde O}(n{sup b}) algorithm that outputs a (0.5 + {delta})-approximation for MaxCut, where {delta} = {delta}(b) is some positive constant. One of the components of our algorithm is a weak local graph partitioning procedure that may be of independent interest. Given a starting vertex i and a conductance parameter {phi}, unless a random walk of length {ell} = O(log n) starting from i mixes rapidly (in terms of {phi} and {ell}), we can find a cut of conductance at most {phi} close to the vertex. The work done per vertex found in the cut is sublinear in n.

Authors:
;  [1]
  1. Yahoo! Research, Santa Clara, CA
Publication Date:
Research Org.:
Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1030363
Report Number(s):
SAND2010-7915C
TRN: US201124%%148
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Conference
Resource Relation:
Conference: Proposed for presentation at the ICS 2010 Conference held January 7-9, 2011 in Beijing, China.
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; APPROXIMATIONS; SANDIA NATIONAL LABORATORIES

Citation Formats

Seshadhri, Comandur, and Kale, Satyen. Combinatorial approximation algorithms for MAXCUT using random walks.. United States: N. p., 2010. Web.
Seshadhri, Comandur, & Kale, Satyen. Combinatorial approximation algorithms for MAXCUT using random walks.. United States.
Seshadhri, Comandur, and Kale, Satyen. 2010. "Combinatorial approximation algorithms for MAXCUT using random walks.". United States.
@article{osti_1030363,
title = {Combinatorial approximation algorithms for MAXCUT using random walks.},
author = {Seshadhri, Comandur and Kale, Satyen},
abstractNote = {We give the first combinatorial approximation algorithm for MaxCut that beats the trivial 0.5 factor by a constant. The main partitioning procedure is very intuitive, natural, and easily described. It essentially performs a number of random walks and aggregates the information to provide the partition. We can control the running time to get an approximation factor-running time tradeoff. We show that for any constant b > 1.5, there is an {tilde O}(n{sup b}) algorithm that outputs a (0.5 + {delta})-approximation for MaxCut, where {delta} = {delta}(b) is some positive constant. One of the components of our algorithm is a weak local graph partitioning procedure that may be of independent interest. Given a starting vertex i and a conductance parameter {phi}, unless a random walk of length {ell} = O(log n) starting from i mixes rapidly (in terms of {phi} and {ell}), we can find a cut of conductance at most {phi} close to the vertex. The work done per vertex found in the cut is sublinear in n.},
doi = {},
url = {https://www.osti.gov/biblio/1030363}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon Nov 01 00:00:00 EDT 2010},
month = {Mon Nov 01 00:00:00 EDT 2010}
}

Conference:
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