Optimal Systolic Design for the Transitive Closure and the Shortest Path Problems
IEEE Transactions on Computers
Minimum-cost spanning tree as a path-finding problem
Information Processing Letters
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
On the PVM Computations of Transitive Closure and Algebraic Path Problems
Proceedings of the 5th European PVM/MPI Users' Group Meeting on Recent Advances in Parallel Virtual Machine and Message Passing Interface
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We present new approaches to the parallel computation of a class of problems related to the GENERIC TRANSITIVE CLOSURE problem (TC, in short). We identify the main ingredient of the TC problem called the MAX-CLOSURE Problem and concentrate on parallel computation of this subproblem, also we show how to reduce TC to matrix multiplication once the MAX-CLOSURE is computed. We present a new variation of the Warshall algorithm for MAX-CLOSURE, both in fine-grained and coarse-grained forms; the coarse-grained version, appropriate for parallel implementation in PVM is especially designed so as to consist of highly parellelisable submatrix multiplications. We used existing, especially efficient PVM subroutines to realise our new MAX-CLOSURE and TC algorithms; the experimental results show that the new algorithms achieve considerable improvement compared to previously known ones.