
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
Antonio Fernández, Kemal Efe, "Generalized Algorithm for Parallel Sorting on Product Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 8, no. 12, pp. 12111225, December, 1997.  
BibTex  x  
@article{ 10.1109/71.640013, author = {Antonio Fernández and Kemal Efe}, title = {Generalized Algorithm for Parallel Sorting on Product Networks}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {8}, number = {12}, issn = {10459219}, year = {1997}, pages = {12111225}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.640013}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Parallel and Distributed Systems TI  Generalized Algorithm for Parallel Sorting on Product Networks IS  12 SN  10459219 SP1211 EP1225 EPD  12111225 A1  Antonio Fernández, A1  Kemal Efe, PY  1997 KW  Sorting KW  interconnection networks KW  product networks KW  algorithms KW  oddeven merge. VL  8 JA  IEEE Transactions on Parallel and Distributed Systems ER   
Abstract—We generalize the wellknown oddeven merge sorting algorithm, originally due to Batcher [2], and show how this generalized algorithm can be applied to sorting on product networks.
If
For product networks with bounded
We show how to apply the algorithm to several cases of wellknown product networks, as well as others introduced recently. We compare the performance of our algorithm to wellknown algorithms developed specifically for these networks, as well as others. The result of these comparisons led us to conjecture that the proposed algorithm is probably the best deterministic algorithm that can be found in terms of the low asymptotic complexity with a small constant.
[1] A. Aggarwal and M.D.A. Huang, "Network Complexity of Sorting and Graph Problems and Simulating CRCW PRAMS by Interconnection Networks," Proc. Third Aegean Workshop Computing, AWOC '88: VLSI Algorithms and Architectures, J.H. Reif, ed., Lecture Notes in Computer Science, vol. 319, pp. 339350,Corfu, Greece. SpringerVerlag, July 1988.
[2] K. Batcher, "Sorting Networks and their Applications," Proc. AFIPS Spring JointComputing Conf., vol. 32, pp. 307314, 1968.
[3] K.E. Batcher, "On Bitonic Sorting Networks," Proc. 1990 Int'l Conf. Parallel Processing, vol. I, pp. 376379, 1990.
[4] M. Baumslag and F. Annexstein, "A Unified Framework for OffLine Permutation Routing in Parallel Networks," Math. Systems Theory, vol. 24, no. 4, pp. 233251, 1991.
[5] G.E. Blelloch, C.E. Leiserson, B.M. Maggs, C.G. Plaxton, S. Smith, and M. Zagha, "A Comparison of Sorting Algorithms for the Connection Machine CM2," Proc. Third Ann. ACM Symp. Parallel Algorithms and Architectures, pp. 316, July 1991.
[6] R. Cypher and C.G. Plaxton, "Deterministic Sorting in Nearly Logarithmic Time on the Hypercube and Related Computers," J. Computer and System Sciences, vol. 47, pp. 501548, Dec. 1993.
[7] R.L.S. Drysdale III and F.H. Young, "Improved Divide/Sort/Merge Sorting Network," SIAM J. Computing, vol. 4, pp. 264270, Sept. 1975.
[8] K. Efe and A. Fernández, "MeshConnected Trees: A Bridge Between Grids and Meshes of Trees," IEEE Trans. Parallel and Distributed Systems, vol. 7, no. 12, pp. 1,2811,291, Dec. 1996.
[9] K. Efe and A. Fernández, "Products of Networks with Logarithmic Diameter and Fixed Degree," IEEE Trans. Parallel and Distributed Systems, vol. 6, pp. 963975, Sept. 1995.
[10] A. Fernández and K. Efe, "Efficient VLSI Layouts for Homogeneous Product Networks," IEEE Trans. Computers, vol. 46, no. 10, pp. 1,0701,082, Oct. 1997.
[11] A. Fernández, K. Efe, A.L. Broadwater, M.A. Lorenzo, and D. Calzada, "A Unified Approach to Algorithm Development for Product Networks," Math. Modelling and Scientific Computing, to appear, vol. 8, 1997.
[12] T. ElGhazawi and A. Youssef, "A General Framework for Developing Adaptive FaultTolerant Routing Algorithms," IEEE Trans. Reliability, vol. 42, pp. 250258, June 1993.
[13] A. Fernández, "Homogeneous Product Networks for Processor Interconnection," PhD thesis, Univ. of Southwestern Louisiana, Lafayette, Oct. 1994.
[14] M.W. Green, "Some Improvements in NonAdaptative Sorting Algorithms," Proc. Sixth Princeton Conf. Information Sciences and Systems, pp. 387391, 1972.
[15] D. Knuth, The Art of Computer Programming, vol. 3: Sorting and Searching. AddisonWesley, 1973.
[16] M. Kunde,“Optimal sorting on multidimensionally mesh connected computers,”inProc. 4th Symp. Theoretical Aspects on Comput. Lecture Notes in Comput. Sci. 247, 1987, pp. 408–419.
[17] D.L. Lee and K.E. Batcher, "A Multiway Merge Sorting Network," IEEE Trans. Parallel and Distributed Systems, vol. 6, no. 2, pp. 211215, Feb. 1995.
[18] D.L. Lee and K.E. Batcher, "On Sorting Multiple Bitonic Sequences," Proc. 1994 Int'l Conf. Parallel Processing, vol. I, pp. 121125, Aug. 1994.
[19] F.T. Leighton,Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes.San Mateo, Calif.: Morgan Kaufmann, 1992.
[20] T. Leighton, "Tight Bounds on the Complexity of Parallel Sorting," IEEE Trans. Computers, vol. 34, no. 4, pp. 344354, Apr. 1985.
[21] K.J. Liszka and K.E. Batcher, "A Modulo Merge Sorting Network," Proc. Fourth Symp. Frontiers of Massively Parallel Computation,McLean, Va., pp. 164169, Oct. 1992.
[22] K.J. Liszka and K.E. Batcher, "A Generalized Bitonic Sorting Network," Proc. 1993 Int'l Conf. Parallel Processing, vol. I, pp. 105108, 1993.
[23] D. Nassimi and S. Sahni, "Bitonic Sort on a MeshConnected Parallel Computer," IEEE Trans. Computers, vol. 27, no. 1, pp. 27, Jan. 1979.
[24] T. Nakatani, S.T. Huang, B.W. Arden, and S.K. Tripathi, "KWay Bitonic Sort," IEEE Trans. Computers, vol. 38, no. 2, pp. 283288, Feb. 1989.
[25] D. Nath, S.N. Maheshwari, and P.C.P. Bhatt, "Efficient VLSI Networks for Parallel Processing Based on Orthogonal Trees," IEEE Trans. Computers, vol. 32, no. 6, pp. 569581, June 1983.
[26] S.R. Öhring and S.K. Das, "The Folded Petersen Cube Network: New Competitors for the Hypercubes," IEEE Trans. Parallel and Distributed Systems, vol. 7, no. 2, pp. 151168, Feb. 1996.
[27] B. Parker and I. Parberry, "Constructing Sorting Networks fromkSorters," Information Processing Letters, vol. 33, pp. 157162, Nov. 1989.
[28] F.P. Preparata and J. Vuillemin, “The CubeConnected Cycles: A Versatile Network for Parallel Computation,” Comm ACM, vol. 24, no. 5, pp. 300309, 1981.
[29] A.L. Rosenberg,“Productshuffle networks: Toward reconciling shuffles and butterflies,” Discrete Applied Mathematics, vol. 37/38, pp. 465488, July 1992.
[30] 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.
[31] H. Stone, "Parallel Processing with the Perfect Shuffle," IEEE Trans. Computers, vol. 20, no. 2, pp. 153161, Feb. 1971.
[32] C. Thompson and H. Kung,“Sorting on a mesh connected parallel computer,”Commun. ACM, vol. 20, pp. 263–271, 1977.
[33] S.S. Tseng and R.C.T. Lee, "A Parallel Sorting Scheme whose Basic Operation Sorts n Elements," Int'l J. Computer and Information Sciences, vol. 14, no. 6, pp. 455467, 1985.
[34] D.C. van Voorhis, "An Economical Construction for Sorting Networks," Proc. AFIPS Nat'l Computer Conf., vol. 43, pp. 921927, 1974.