Coarse grained parallel maximum matching in convex bipartite graphs

We present a coarse grained parallel algorithm for computing a maximum matching in a convex bipartite graph G=(A,B,E). For p processors with N/p memory per processor, N=|A|+|B|,N/p/spl ges/p, the algorithm requires O(log p) communication rounds and O(T/sub sequ/(n/p,m/p)+n/p log p) local computation, where n=|A|,m=|B| and T/sub sequ/(n,m) is the sequential time complexity for the problem. For the BSP model, this implies O(log p) supersteps with O(gN+gn/p log p) communication cost and O(T/sub sequ/(n/p,m/p)+n/p log p) local computation.

[1]  Richard M. Karp,et al.  A n^5/2 Algorithm for Maximum Matchings in Bipartite Graphs , 1971, SWAT.

[2]  Lawrence Snyder,et al.  Type architectures, shared memory, and the corollary of modest potential , 1986 .

[3]  Leslie G. Valiant,et al.  A bridging model for parallel computation , 1990, CACM.

[4]  F. Glover.  Maximum matching in a convex bipartite graph , 1967 .

[5]  Michael T. Goodrich,et al.  Communication-Efficient Parallel Sorting , 1999, SIAM J. Comput..

[6]  Kenneth C. SevcikComputer.  Parallel Sorting by Overpartitioning , 1994 .

[7]  Xiaotie Deng,et al.  Efficient routing and message bounds for optimal parallel algorithms , 1995, Proceedings of 9th International Parallel Processing Symposium.

[8]  F. Dehne,et al.  A NOTE ON COARSE GRAINED PARALLEL INTEGER SORTING , 1999 .

[9]  Xiaotie Deng.  A Convex Hull Algorithm on Coarse-Grained Multiprocessors , 1994, ISAAC.

[10]  Richard M. Karp,et al.  A n^5/2 Algorithm for Maximum Matchings in Bipartite Graphs , 1971, SWAT.

[11]  Xiaotie Deng,et al.  A randomized parallel 3D convex hull algorithm for coarse grained multicomputers , 1995, SPAA '95.

[12]  Richard J. Anderson,et al.  A comparison of shared and nonshared memory models of parallel computation , 1991 .

[13]  Xiaotie Deng,et al.  Good algorithm design style for multiprocessors , 1994, Proceedings of 1994 6th IEEE Symposium on Parallel and Distributed Processing.

[14]  Andrew Rau-Chaplin,et al.  Scalable parallel geometric algorithms for coarse grained multicomputers , 1993, SCG '93.

[15]  Guy E. Blelloch,et al.  A comparison of sorting algorithms for the connection machine CM-2 , 1991, SPAA '91.

[16]  Afonso Ferreira,et al.  Efficient Parallel Graph Algorithms for Coarse-Grained Multicomputers and BSP , 2002, Algorithmica.

[17]  Albert Chan,et al.  A Note on Coarse Grained Parallel Integer Sorting , 1999, Parallel Process. Lett..

[18]  Sartaj Sahni,et al.  A parallel matching algorithm for convex bipartite graphs and applications to scheduling , 1984, J. Parallel Distributed Comput..

[19]  Leslie G. Valiant,et al.  Direct Bulk-Synchronous Parallel Algorithms , 1992, J. Parallel Distributed Comput..

[20]  Hui Li,et al.  Parallel sorting by over partitioning , 1994, SPAA '94.