Off-line permutation scheduling on circuit-switched fixed routing networks

The problem of offline permutation scheduling on linear arrays, rings, hypercubes, and two-dimensional arrays, assuming the CSFR (circuit-switched fixed routing) model, is examined. Optimal permutation scheduling involves finding a minimum number of subsets of nonconflicting source-destination paths. Every subset of paths can be established to run in one pass. Optimal permutation scheduling on linear arrays is shown to be linear and on rings NP-complete. On hypercubes, the problem is NP-complete. However, the author discusses an O(N log N) algorithm that routes any permutation in two passes if the model is relaxed to allow for two routing rules, the e-cube rule and the e/sup -1/-cube rule. This complexity is reduced to O(N) hypercube-parallel time. An O(N log/sup 2/ N) bipartite-matching-based algorithm designed to schedule any permutation on p*q meshes/tori in q passes is considered.<<ETX>>

[1]  Viktor K. Prasanna,et al.  Permutations on Illiac IV-Type Networks , 1986, IEEE Transactions on Computers.

[2]  Leslie G. Valiant,et al.  A fast parallel algorithm for routing in permutation networks , 1981, IEEE Transactions on Computers.

[3]  Leslie G. Valiant,et al.  A Scheme for Fast Parallel Communication , 1982, SIAM J. Comput..

[4]  Kyungsook Y. Lee,et al.  A New Benes Network Control Algorithm , 1987, IEEE Trans. Computers.

[5]  Sartaj Sahni,et al.  An optimal routing algorithm for mesh-connected Parallel computers , 1980, JACM.

[6]  Frank Harary,et al.  On the group of the composition of two graphs , 1959 .

[7]  Allan Gottlieb,et al.  Complexity Results for Permuting Data and Other Computations on Parallel Processors , 1984, JACM.

[8]  Gary L. Miller,et al.  The Complexity of Coloring Circular Arcs and Chords , 1980, SIAM J. Algebraic Discret. Methods.

[9]  Cauligi S. Raghavendra,et al.  On Self-Routing in Benes and Shuffle-Exchange Networks , 1991, IEEE Trans. Computers.

[10]  Duncan H. Lawrie,et al.  Access and Alignment of Data in an Array Processor , 1975, IEEE Transactions on Computers.

[11]  Joseph Y.-T. Leung,et al.  Efficient algorithms for interval graphs and circular-arc graphs , 1982, Networks.

[12]  Sartaj Sahni,et al.  A Self-Routing Benes Network and Parallel Permutation Algorithms , 1981, IEEE Transactions on Computers.

[13]  Joseph Y.-T. Leung,et al.  An Optimal Solution for the Channel-Assignment Problem , 1979, IEEE Transactions on Computers.

[14]  Abdou Youssef.  Online communication on circuit-switched fixed routing meshes , 1992, Proceedings Sixth International Parallel Processing Symposium.