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:
-
- 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}
}