Efficient parallel algorithms for a class of graph theoretic problems
SIAM Journal on Computing
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IEEE Transactions on Computers
An introduction to parallel algorithms
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Finding a smallest augmentation to biconnect a graph
SIAM Journal on Computing
Biconnectivity approximations and graph carvings
Journal of the ACM (JACM)
Efficient parallel algorithms for finding biconnected components of some intersection graphs
CSC '91 Proceedings of the 19th annual conference on Computer Science
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Communications of the ACM
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Journal of Parallel and Distributed Computing
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Better speedups using simpler parallel programming for graph connectivity and biconnectivity
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Techniques for designing efficient parallel graph algorithms for SMPs and multicore processors
ISPA'07 Proceedings of the 5th international conference on Parallel and Distributed Processing and Applications
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We present an experimental study of parallel biconnected components algorithms employing several fundamental parallel primitives, e.g., prefix sum, list ranking, sorting, connectivity, spanning tree, and tree computations. Previous experimental studies of these primitives demonstrate reasonable parallel speedups. However, when these algorithms are used as subroutines to solve higher-level problems, there are two factors that hinder fast parallel implementations. One is parallel overhead, i.e., the large constant factors hidden in the asymptotic bounds; the other is the discrepancy among the data structures used in the primitives that brings non-negligible conversion cost. We present various optimization techniques and a new parallel algorithm that significantly improve the performance of finding biconnected components of a graph on symmetric multiprocessors (SMPs). Finding biconnected components has application in fault-tolerant network design, and is also used in graph planarity testing. Our parallel implementation achieves speedups up to 4 using 12 processors on a Sun E4500 for large, sparse graphs, and the source code is freely-available at our web site http://www.ece.unm.edu/~dbader.