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Title: Efficient Approximation Algorithms for Weighted $$b$$-Matching

Abstract

We describe a half-approximation algorithm, b-Suitor, for computing a b-Matching of maximum weight in a graph with weights on the edges. b-Matching is a generalization of the well-known Matching problem in graphs, where the objective is to choose a subset of M edges in the graph such that at most a speci ed number b(v) of edges in M are incident on each vertex v. Subject to this restriction we maximize the sum of the weights of the edges in M. We prove that the b-Suitor algorithm computes the same b-Matching as the one obtained by the greedy algorithm for the problem. We implement the algorithm on serial and shared-memory parallel processors, and compare its performance against a collection of approximation algorithms that have been proposed earlier. Our results show that the b-Suitor algorithm outperforms the Greedy and Locally Dominant edge algorithms by one to two orders of magnitude on a serial processor. The b-Suitor algorithm has a high degree of concurrency, and it scales well up to 240 threads on a shared memory multiprocessor. The b-Suitor algorithm outperforms the Locally Dominant edge algorithm by a factor of fourteen on 16 cores of an Intel Xeon multiprocessor.

Authors:
 [1];  [1];  [2];  [2];  [2];  [3];  [4];  [2]
  1. Purdue Univ., West Lafayette, IN (United States). Dept. of Computer Science
  2. Intel Labs, Santa Clara, CA (United States)
  3. Univ. of Bergen, Bergen (Norway). Dept. of Informatics
  4. Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
National Science Foundation (NSF); USDOE
OSTI Identifier:
1418504
Grant/Contract Number:  
SC0010205; CCF-1552323
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
SIAM Journal on Scientific Computing
Additional Journal Information:
Journal Volume: 38; Journal Issue: 5; Journal ID: ISSN 1064-8275
Publisher:
SIAM
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Khan, Arif, Pothen, Alex, Mostofa Ali Patwary, Md., Satish, Nadathur Rajagopalan, Sundaram, Narayanan, Manne, Fredrik, Halappanavar, Mahantesh, and Dubey, Pradeep. Efficient Approximation Algorithms for Weighted $b$-Matching. United States: N. p., 2016. Web. doi:10.1137/15M1026304.
Khan, Arif, Pothen, Alex, Mostofa Ali Patwary, Md., Satish, Nadathur Rajagopalan, Sundaram, Narayanan, Manne, Fredrik, Halappanavar, Mahantesh, & Dubey, Pradeep. Efficient Approximation Algorithms for Weighted $b$-Matching. United States. https://doi.org/10.1137/15M1026304
Khan, Arif, Pothen, Alex, Mostofa Ali Patwary, Md., Satish, Nadathur Rajagopalan, Sundaram, Narayanan, Manne, Fredrik, Halappanavar, Mahantesh, and Dubey, Pradeep. 2016. "Efficient Approximation Algorithms for Weighted $b$-Matching". United States. https://doi.org/10.1137/15M1026304. https://www.osti.gov/servlets/purl/1418504.
@article{osti_1418504,
title = {Efficient Approximation Algorithms for Weighted $b$-Matching},
author = {Khan, Arif and Pothen, Alex and Mostofa Ali Patwary, Md. and Satish, Nadathur Rajagopalan and Sundaram, Narayanan and Manne, Fredrik and Halappanavar, Mahantesh and Dubey, Pradeep},
abstractNote = {We describe a half-approximation algorithm, b-Suitor, for computing a b-Matching of maximum weight in a graph with weights on the edges. b-Matching is a generalization of the well-known Matching problem in graphs, where the objective is to choose a subset of M edges in the graph such that at most a speci ed number b(v) of edges in M are incident on each vertex v. Subject to this restriction we maximize the sum of the weights of the edges in M. We prove that the b-Suitor algorithm computes the same b-Matching as the one obtained by the greedy algorithm for the problem. We implement the algorithm on serial and shared-memory parallel processors, and compare its performance against a collection of approximation algorithms that have been proposed earlier. Our results show that the b-Suitor algorithm outperforms the Greedy and Locally Dominant edge algorithms by one to two orders of magnitude on a serial processor. The b-Suitor algorithm has a high degree of concurrency, and it scales well up to 240 threads on a shared memory multiprocessor. The b-Suitor algorithm outperforms the Locally Dominant edge algorithm by a factor of fourteen on 16 cores of an Intel Xeon multiprocessor.},
doi = {10.1137/15M1026304},
url = {https://www.osti.gov/biblio/1418504}, journal = {SIAM Journal on Scientific Computing},
issn = {1064-8275},
number = 5,
volume = 38,
place = {United States},
year = {Fri Jan 01 00:00:00 EST 2016},
month = {Fri Jan 01 00:00:00 EST 2016}
}

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