Multithreaded Algorithms for Maximum Matching in Bipartite Graphs

We design, implement, and evaluate algorithms for computing a matching of maximum cardinality in a bipartite graph on multicore and massively multithreaded computers. As computers with larger numbers of slower cores dominate the commodity processor market, the design of multithreaded algorithms to s...

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Vydáno v:2012 IEEE 26th International Parallel and Distributed Processing Symposium s. 860 - 872
Hlavní autoři: Azad, A., Halappanavar, M., Rajamanickam, S., Boman, E. G., Khan, A., Pothen, A.
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 01.05.2012
Témata:
Algorithm design and analysis
Arrays
Bipartite graph
bipartite graphs
Heuristic algorithms
Instruction sets
maximum cardinality matchings
Multicore processing
multithreaded algorithm
parallel algorithm
Parallel algorithms
ISBN:1467309753, 9781467309752
ISSN:1530-2075
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Shrnutí:We design, implement, and evaluate algorithms for computing a matching of maximum cardinality in a bipartite graph on multicore and massively multithreaded computers. As computers with larger numbers of slower cores dominate the commodity processor market, the design of multithreaded algorithms to solve large matching problems becomes a necessity. Recent work on serial algorithms for the matching problem has shown that their performance is sensitive to the order in which the vertices are processed for matching. In a multithreaded environment, imposing a serial order in which vertices are considered for matching would lead to loss of concurrency and performance. But this raises the question: {\em Would parallel matching algorithms on multithreaded machines improve performance over a serial algorithm?}We answer this question in the affirmative. We report efficient multithreaded implementations of three classes of algorithms based on their manner of searching for augmenting paths: breadth-first-search, depth-first-search, and a combination of both. The Karp-Sipser initialization algorithm is used to make the parallel algorithms practical. We report extensive results and insights using three shared-memory platforms (a 48-core AMD Opteron, a 32-coreIntel Nehalem, and a 128-processor Cray XMT) on a representative set of real-world and synthetic graphs. To the best of our knowledge, this is the first study of augmentation-based parallel algorithms for bipartite cardinality matching that demonstrates good speedups on multithreaded shared memory multiprocessors.
ISBN:1467309753
9781467309752
ISSN:1530-2075
DOI:10.1109/IPDPS.2012.82