This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Multiway Merging in Parallel
January 1996 (vol. 7 no. 1)
pp. 11-17

Abstract—The problem of merging k (k≥ 2) sorted lists is considered. We give an optimal parallel algorithm which takes $O({\textstyle{{n\log k} \over p}}+\log n)$ time using p processors on a parallel random access machine that allows concurrent reads and exclusive writes, where n is the total size of the input lists. This algorithm achieves O(log n) time using $p={\textstyle{{n\log k} \over {\log n}}}$ processors. Most of the previous research for this problem has been focused on the case when k = 2. Very recently, parallel solutions for the case when k > 2 have been reported. Our solution is the first logarithmic time optimal parallel algorithm for the problem when k≥ 2. It can also be seen as a unified optimal parallel algorithm for sorting and merging. In order to support the algorithm, a new processor assignment strategy is also presented.

[1] M. Ajtai,J. Komlos,W.L. Steiger, and E. Szemeredi,"An O(n log n) sorting network," Proc. Ann. ACM Symp. Theory of Computing, pp. 1-9, 1983.
[2] S.G. Akl, The Design and Analysis of Parallel Algorithms. Orlando, Fl.: Academic Press, 1989.
[3] S.G. Akl and N. Santoro,"Optimal parallel merging and sorting without memory conflict," IEEE Trans. Computers, vol. 36, no. 11, pp. 1,367-1,369, 1987.
[4] K.E. Batcher,"Sorting networks and their applications," Proc. AFIPS Spring Joint Computer Conf. 32, pp. 307-314, 1968.
[5] D. Bitton,D.J. Dewitt,D.K. Hsiao, and J. Menon,"A taxonomy of parallel sorting," ACM Computing Surveys, vol. 16, pp. 287-318, 1984.
[6] A. Borodin and J.E. Hopcroft,"Routing, merging and sorting on parallel models of comparison," J. Computer and System Science, vol. 30, pp. 130-145, 1985.
[7] R. Cole, "Parallel Merge Sort," SIAM J. Computing, vol. 17, pp. 770-785, 1988.
[8] R. Cole and U. Vishkin, "Approximate Parallel Scheduling. Part 1: The Basic Technique with Applications to Optimal Parallel List Ranking in Logarithmic Time," SIAM J. Computing, vol. 18, pp. 128-142, 1988.
[9] E. Dekel and I. Ozsvath,"Parallel external sorting," J. Parallel and Distributed Computing, vol. 6, pp. 623-635, 1989.
[10] J.Y. Fu and F.C. Lin,"Optimal parallel external merging under hardware constraints," Proc. 1991 Int'l Conf. Parallel Processing, pp. III70-III74, 1991.
[11] T. Hagerup and C. Rub,"Optimal merging and sorting on the EREW PRAM," Information Processing Letters, vol. 33, pp. 181-185, 1989.
[12] D.E. Knuth, The Art of Computer Programming, vol. 1,Addison Wesley, second ed. 1973.
[13] G. Salton, Automatic Text Processing: The Transformation, Analysis, and Retrieval of Information by Computer, Addison Wesley, New York, 1989.
[14] Y. Shiloach and U. Vishkin,"Finding the maximum, merging and sorting in a parallel computation," J. Algorithms, vol. 2, pp. 88-102, 1981.
[15] P. Valduriez and G. Gardarin,“Join and semijoin algorithms for a multiprocessor database machine,” ACM Trans. on Database Systems, vol. 9, no. 1, pp. 133-161, Mar. 1984.
[16] P.J. Varman,S.D. Scheufler,B.R. Iyer, and G.R. Ricard,"Merging multiple lists on hierarchical-memory multiprocessors," J. Parallel and Distributed Computing, vol. 12, pp. 171-177, 1991.

Index Terms:
Analysis of algorithms, databases, information retrieval, merging, parallel computation, processors assignment, sorting.
Citation:
Zhaofang Wen, "Multiway Merging in Parallel," IEEE Transactions on Parallel and Distributed Systems, vol. 7, no. 1, pp. 11-17, Jan. 1996, doi:10.1109/71.481593
Usage of this product signifies your acceptance of the Terms of Use.