Computing Maximum Cardinality Matchings in Parallel on Bipartite Graphs via Tree-Grafting

Journal Article · Thu Mar 24 04:00:00 EDT 2016 · IEEE Transactions on Parallel and Distributed Systems

DOI:https://doi.org/10.1109/TPDS.2016.2546258· OSTI ID:1379627

Azad, Ariful ^[1]; Buluc, Aydn ^[1]; Pothen, Alex ^[2]

---

1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computatoinal Research Division
2. Purdue Univ., West Lafayette, IN (United States). Dept. of Computer Science

It is difficult to obtain high performance when computing matchings on parallel processors because matching algorithms explicitly or implicitly search for paths in the graph, and when these paths become long, there is little concurrency. In spite of this limitation, we present a new algorithm and its shared-memory parallelization that achieves good performance and scalability in computing maximum cardinality matchings in bipartite graphs. This algorithm searches for augmenting paths via specialized breadth-first searches (BFS) from multiple source vertices, hence creating more parallelism than single source algorithms. Algorithms that employ multiple-source searches cannot discard a search tree once no augmenting path is discovered from the tree, unlike algorithms that rely on single-source searches. We describe a novel tree-grafting method that eliminates most of the redundant edge traversals resulting from this property of multiple-source searches. We also employ the recent direction-optimizing BFS algorithm as a subroutine to discover augmenting paths faster. Our algorithm compares favorably with the current best algorithms in terms of the number of edges traversed, the average augmenting path length, and the number of iterations. Here, we provide a proof of correctness for our algorithm. Our NUMA-aware implementation is scalable to 80 threads of an Intel multiprocessor and to 240 threads on an Intel Knights Corner coprocessor. On average, our parallel algorithm runs an order of magnitude faster than the fastest algorithms available. The performance improvement is more significant on graphs with small matching number.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
• DOE Contract Number: AC02-05CH11231; SC0010205
• OSTI ID: 1379627
• Journal Information: IEEE Transactions on Parallel and Distributed Systems, Journal Name: IEEE Transactions on Parallel and Distributed Systems Journal Issue: 1 Vol. 28; ISSN 1045-9219
• Publisher: IEEE
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
bipartite graph
cardinality matching
parallel algorithms
tree grafting