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:
-
- Purdue Univ., West Lafayette, IN (United States). Dept. of Computer Science
- Intel Labs, Santa Clara, CA (United States)
- Univ. of Bergen, Bergen (Norway). Dept. of Informatics
- 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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