Parallel recognition and decomposition of two terminal series parallel graphs
Information and Computation
A bridging model for parallel computation
Communications of the ACM
Parallel recognition of the consecutive ones property with applications
Journal of Algorithms
Scalable parallel geometric algorithms for coarse grained multicomputers
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
A randomized parallel 3D convex hull algorithm for coarse grained multicomputers
Proceedings of the seventh annual ACM symposium on Parallel algorithms and architectures
Graph Isomorphism and Identification Matrices: Parallel Algorithms
IEEE Transactions on Parallel and Distributed Systems
Communication-efficient parallel sorting (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Synthesis of Parallel Algorithms
Synthesis of Parallel Algorithms
Coarse Grained Parallel Maximum Matching In Convex Bipartite Graphs
IPPS '99/SPDP '99 Proceedings of the 13th International Symposium on Parallel Processing and the 10th Symposium on Parallel and Distributed Processing
Efficient Parallel Graph Algorithms For Coarse Grained Multicomputers and BSP
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Efficient parallel algorithms for chordal graphs
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Journal of Computer and System Sciences
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In this paper, we present parallel algorithms for the coarse grained multicomputer (CGM) and the bulk synchronous parallel computer (BSP) for solving two well known graph problems: (1) determining whether a graph G is bipartite, and (2) determining whether a bipartite graph G is convex. Our algorithms require O(log p) and O(log2 p) communication rounds, respectively, and linear sequential work per round on a CGM with p processors and N/p local memory per processor, N=|G|. The algorithms assume that N/p ≥ pƐ for some fixed Ɛ 0, which is true for all commercially available multiprocessors. Our results imply BSP algorithms with O(log p) and O(log2 p) supersteps, respectively, O(g log(p)N/p) communication time, and O(log(p)N/p) local computation time. Our algorithm for determining whether a bipartite graph is convex includes a novel, coarse grained parallel, version of the PQ tree data structure introduced by Booth and Lueker. Hence, our algorithm also solves, with the same time complexity as indicated above, the problem of testing the consecutive-ones property for (0, 1) matrices as well as the chordal graph recognition problem. These, in turn, have numerous applications in graph theory, DNA sequence assembly, database theory, and other areas.