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

Journal Article · Fri Jan 01 00:00:00 EST 2016 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/15M1026304· OSTI ID:1418504

Khan, Arif ^[1]; Pothen, Alex ^[1]; Mostofa Ali Patwary, Md. ^[2]; Satish, Nadathur Rajagopalan ^[2]; Sundaram, Narayanan ^[2]; Manne, Fredrik ^[3]; Halappanavar, Mahantesh ^[4]; Dubey, Pradeep ^[2]

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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)

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.

• Research Organization: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
• Sponsoring Organization: National Science Foundation (NSF); USDOE
• Grant/Contract Number: SC0010205
• OSTI ID: 1418504
• Alternate ID(s): OSTI ID: 1337238
• Journal Information: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 5 Vol. 38; ISSN 1064-8275
• Publisher: SIAM
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING