This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Sorting by Parallel Insertion on a One-Dimensional Subbus Array
November 1998 (vol. 47 no. 11)
pp. 1267-1281

Abstract—We consider the problem of sorting on a one-dimensional subbus array of processors, an architecture that communicates using a segmentable bus. The subbus broadcast operation makes possible a new class of parallel sorting algorithms whose complexity we analyze with the parallel insertion model. We give per-input lower bounds for sorting in the parallel insertion model and demonstrate sorting strategies that are optimal by matching those lower bounds. For each of our sorting strategies, we discuss the issues involved in implementing them on subbus machines. Finally, we empirically evaluate the performance of our sorting strategies by applying them to shearsort, a common two-dimensional mesh sorting algorithm. Our results suggest that for sorting the subbus broadcast capability gives at most a slight advantage over using only nearest neighbor communication.

[1] T. Blank, "The MasPar MP-1 Architecture," IEEE Compcon, pp. 20-24. IEEE, San Francisco, Feb./Mar. 1990.
[2] A. Condon, R.E. Ladner, J. Lampe, and R. Sinha, "Complexity of Subbus Mesh Computations," SIAM J. Computing, vol. 25, no. 3, pp. 520-539, 1996.
[3] M.H. DeGroot, Probability and Statistics. Addison-Wesley, 1975, 1986.
[4] H.B. Demuth, "Electronic Data Sorting," PhD thesis, Stanford Univ., Oct. 1956.
[5] H.B. Demuth, "Electronic Data Sorting," EEE Trans. Computers, vol. 34, no. 4, pp. 296-310, Apr. 1985.
[6] J.D. Fix and R.E. Ladner, "Optimal One-Way Sorting on a One-Dimensional Subbus Array," Proc. Sixth Ann. ACM-SIAM Symp. Discrete Algorithms, pp. 586-594, Jan. 1995.
[7] N. Haberman, "Parallel Neighbor-Sort (or the Glory of the Induction Principle)," Technical Report AD-759 248, Nat'l Technical Information Service, 1972.
[8] D.E. Knuth, The Art of Computer Programming, vol. 1,Addison Wesley, second ed. 1973.
[9] D. Knuth, The Art of Computer Programming, vol. 3: Sorting and Searching. Addison-Wesley, 1973.
[10] F.T. Leighton,Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes.San Mateo, Calif.: Morgan Kaufmann, 1992.
[11] J.Y-T. Leung and S.M. Shende, "On Multi-Dimensional Packet Routing for Meshes with Buses," J. Parallel and Distributed Computing, vol. 20, no. 2, pp. 187-197, 1994.
[12] R. Miller,V.K. Prasanna Kumar,D.I. Reisis, and Q.F. Stout,“Parallel computations on reconfigurable meshes,” IEEE Trans. on Computers, pp. 678-692, June 1993.
[13] V.K. Prasanna Kumar, and C.S. Raghavendra,“Array processor with multiple broadcasting,” J. of Parallel and Distributed Computing, vol. 4, pp. 173-190, 1987.
[14] S. Rajasekaran, "Mesh Connected Computers with Fixed and Reconfigurable Buses: Packet Routing and Sorting," IEEE Trans. Computers, vol. 45, no. 5, pp. 529-539, May 1996.
[15] K. Sado and Y. Igarashi, "Some Parallel Sorts on a Mesh-Connected Processor Array and Their Time Efficiency," J. Parallel and Distributed Computing, vol. 3, pp. 398-410, 1986.
[16] I. Scherson, S. Sen, and A. Shamir, "Shear-Sort: A True Two-Dimensional Sorting Technique for VLSI Networks," IEEE-ACM Int'l Conf. Parallel Processing, pp. 903-908, 1986.
[17] C. Schnorr and A. Shamir,“An optimal sorting algorithm for mesh connected computers,”inProc. 18th ACM Symp. on Theory of Comput., 1986, pp. 263–271.
[18] Q.F. Stout, "Mesh Connected Computers with Broadcasting," IEEE Trans. Computers, vol. 32, no. 9, pp. 826-830, Sept. 1983.

Index Terms:
Subbus array, sorting, parallel algorithms, lower bounds, segmented-bus architecture, reconfigurable mesh architecture, odd-even transposition sort, bubble sort.
Citation:
James D. Fix, Richard E. Ladner, "Sorting by Parallel Insertion on a One-Dimensional Subbus Array," IEEE Transactions on Computers, vol. 47, no. 11, pp. 1267-1281, Nov. 1998, doi:10.1109/12.736441
Usage of this product signifies your acceptance of the Terms of Use.