Erik G. Boman

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 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.

Combinatorial Algorithms to Enable Computational Science and Engineering: Work from the CSCAPES Institute

This final progress report summarizes the work accomplished at the Combinatorial Scientific Computing and Petascale Simulations Institute. We developed Zoltan, a parallel mesh partitioning library that made use of accurate hyeprgraph models to provide load balancing in mesh-based computations. We developed several graph coloring algorithms for computing Jacobian and Hessian matrices and organized them into a software package called ColPack. We developed parallel algorithms for graph coloring and graph matching problems, and also designed multi-scale graph algorithms. Three PhD students graduated, six more are continuing their PhD studies, and four postdoctoral scholars were advised. Six of these students and Fellows have joined DOE Labs (Sandia, Berkeley, as staff scientists or as postdoctoral scientists. We also organized the SIAM Workshop on Combinatorial Scientific Computing (CSC) in 2007, 2009, and 2011 to continue to foster the CSC community.