Algorithms and Average Time Bounds of Sorting on a Mesh-Connected Computer

We give three new parallel sorting algorithms on a mesh-connected computer with wraparound connections (i.e. a torus). These three algorithms, with the minimum queue size of 1, sort n/sup 2/ random input data items into a blocked snakelike row major order, a row major order, and a snakelike row major order, in 1.5n+o(n), 2n+o(n), and 2n+o(n) average steps, respectively. These results improve the previous results of 2n+o(n), 2.5n+o(n), and 2.5n+o(n), respectively. In addition, we prove that the distance bound n on a torus is an average-time lower bound independent of indexing schemes of sorting random input data items on it. >

[1]  Qian-Ping Gu,et al.  Learning Monotone Boolean Functions by Uniformly Distributed Examples , 1992, SIAM J. Comput..

[2]  Adi Shamir,et al.  An optimal sorting algorithm for mesh connected computers , 1986, STOC '86.

[3]  Peter F. Corbett,et al.  A Unified Algorithm for Sorting on Multidimensional Mesh-Connected Processors , 1991, Inf. Process. Lett..

[4]  Manoj Kumar,et al.  An Efficient Implementation of Batcher's Odd-Even Merge Algorithm and Its Application in Parallel Sorting Schemes , 1983, IEEE Transactions on Computers.

[5]  Vipin Kumar,et al.  Scalability of parallel sorting on mesh multicomputers , 1991, [1991] Proceedings. The Fifth International Parallel Processing Symposium.

[6]  Frank Thomson Leighton,et al.  Average case analysis of greedy routing algorithms on arrays , 1990, SPAA '90.

[7]  Yijie Han,et al.  Indexing functions and time lower bounds for sorting on a mesh-connected computer , 1992, Discret. Appl. Math..

[8]  János Komlós,et al.  An 0(n log n) sorting network , 1983, STOC.

[9]  Isaac D. Scherson,et al.  Parallel Sorting in Two-Dimensional VLSI Models of Computation , 1989, IEEE Trans. Computers.

[10]  Leslie G. Valiant,et al.  Fast probabilistic algorithms for hamiltonian circuits and matchings , 1977, STOC '77.

[11]  Yishay Mansour,et al.  Sorting on a Ring of Processors , 1990, J. Algorithms.

[12]  Jeffrey D Ullma.  Computational Aspects of VLSI , 1984 .

[13]  Selim G. Akl,et al.  Parallel Sorting Algorithms , 1985 .

[14]  Sartaj Sahni,et al.  Bitonic Sort on a Mesh-Connected Parallel Computer , 1979, IEEE Transactions on Computers.

[15]  Manfred Kunde.  Concentrated regular data streams on grids: sorting and routing near to the bisection bound , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[16]  Quentin F. Stout,et al.  Mapping vision algorithms to parallel architectures , 1988, Proc. IEEE.

[17]  Hartmut Schmeck,et al.  Systolic Sorting on a Mesh-Connected Network , 1985, IEEE Transactions on Computers.

[18]  Franco P. Preparata,et al.  A minimum area VLSI network for O(logn) time sorting , 1984, STOC '84.

[19]  Frank Thomson Leighton,et al.  Tight Bounds on the Complexity of Parallel Sorting , 1985, IEEE Trans. Computers.

[20]  Manfred Kunde.  Optimal Sorting on Multi-Dimensionally Mesh-Connected Computers , 1987, STACS.

[21]  H. Chernoff.  A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations , 1952 .

[22]  Christos Kaklamanis,et al.  Randomized sorting and selection on mesh-connected processor arrays (preliminary version) , 1991, SPAA '91.

[23]  Bogdan S. Chlebus.  Sorting within Distance Bound on a Mesh-Connected Processor Array , 1989, Optimal Algorithms.