A simple architecture for constant time sorting machines

In this paper, we propose a constant time sorting algorithm on an array composed of comparators and single-pole-double-throw switches, which is far more feasible than other constant time sorting algorithms [21]-[23]. Our results shown that the algorithm uses time <i>T</i> = &Theta;(1) and area <i>A</i> = <i>O</i>(<i>N</i><sup>3</sup>). This nearly matches the <i>AT</i><sup>2</sup> = &Omega;(<i>N</i><sup>2</sup> log<sup>2</sup> <i>N</i>) lower bound for sorting in the VLSI model.

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

[2]  Wen-Tsuen Chen,et al.  Constant Time Sorting on Reconfigurable Meshes , 1994, IEEE Trans. Computers.

[3]  Peter M. Flanders.  A Unified Approach to a Class of Data Movements on an Array Processor , 1982, IEEE Transactions on Computers.

[4]  Gérard M. Baudet,et al.  Optimal Sorting Algorithms for Parallel Computers , 1978, IEEE Transactions on Computers.

[5]  H. Peter Hofstee,et al.  Distributed Sorting , 1990, Sci. Comput. Program..

[6]  S. N. Maheshwari,et al.  Efficient VLSI Networks for Parallel Processing Based on Orthogonal Trees , 1983, IEEE Transactions on Computers.

[7]  H. T. Kung,et al.  Sorting on a mesh-connected parallel computer , 1977, CACM.

[8]  Gen-Huey Chen,et al.  Constant Time Sorting on a Processor Array with a Reconfigurable Bus System , 1990, Inf. Process. Lett..

[9]  Franco P. Preparata,et al.  A Minimum Area VLSI Network for O(log n) Time Sorting , 1985, IEEE Transactions on Computers.

[10]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[11]  Selim G. Akl,et al.  Design and analysis of parallel algorithms , 1985 .

[12]  Allan Borodin,et al.  Routing, Merging, and Sorting on Parallel Models of Computation , 1985, J. Comput. Syst. Sci..

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

[14]  Clyde P. Kruskal,et al.  Searching, Merging, and Sorting in Parallel Computation , 1983, IEEE Transactions on Computers.

[15]  Sartaj Sahni,et al.  Parallel permutation and sorting algorithms and a new generalized connection network , 1982, JACM.

[16]  Franco P. Preparata,et al.  The cube-connected-cycles: A versatile network for parallel computation , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[17]  Larry Rudolph,et al.  A Robust Sorting Network , 1985, IEEE Transactions on Computers.

[18]  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.

[19]  Kenneth E. Batcher,et al.  Sorting networks and their applications , 1968, AFIPS Spring Joint Computing Conference.

[20]  Harold S. Stone,et al.  Parallel Processing with the Perfect Shuffle , 1971, IEEE Transactions on Computers.

[21]  David E. Muller,et al.  Bounds to Complexities of Networks for Sorting and for Switching , 1975, JACM.

[22]  Franco P. Preparata,et al.  New Parallel-Sorting Schemes , 1978, IEEE Transactions on Computers.

[23]  Harold S. Stone.  Sorting on STAR , 1978, IEEE Transactions on Software Engineering.