This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Optimal Task Assignment in Linear Array Networks
July 1992 (vol. 41 no. 7)
pp. 877-880

The problem of assigning tasks to the processors of a distributed computing system such that the sum of execution and communication costs is minimized is discussed. This problem is known to be NP-complete in the general case, and thus intractable for systems with a large number of processors. H.S. Stone's (1977) network flow approach for a two-processor system is extended to the case for a linear array of any number of processors. The task assignment problem for a linear array network is first transformed into the two-terminal network flow problem, and then solved by applying the Goldberg-Tarjan (1987) network flow algorithm in time no worse than O(n/sup 2/m/sup 3/ log n), where n and m are the number of processors and the number of tasks, respectively.

[1] R. K. Arora and S. P. Rana, "Heuristic methods for process assignment in distributed computing systems,"Inform. Processing Lett., vol. 11, pp. 199-203, Dec. 1980.
[2] S. H. Bokhari, "Dual processor scheduling with dynamic reassignment,"IEEE Trans. Software Eng., vol. SE-5, pp. 341-349, July 1979.
[3] S. H. Bokhari, "A shortest tree algorithm for optimal assignments across space and time in a distributed processor systems,"IEEE Trans. Software Eng., vol. SE-7, pp. 583-589, Nov. 1981.
[4] S. H. Bokhari,Assignment Problems in Parallel and Distributed Computing. Boston, MA: Kluwer Academic, 1987.
[5] S. H. Bokhari, "Partitioning problems in parallel, pipelined and distributed computing,"IEEE Trans. Comput., vol. C-37, pp. 48-57, Jan. 1988.
[6] J. Edmonds and R. M. Karp, "Theoretical improvements in algorithmic efficiency for network flow problems,"J. Ass. Comput. Mach., vol. 19, no. 2, pp. 248-264, Apr. 1972.
[7] L. R. Ford, Jr. and D. R. Fulkerson,Flows in Networks. Princeton, NJ: Princeton Univ. Press, 1962.
[8] A. Goldberg and R. Tarjan, "A new approach to the maximum flow problem," inProc. 18th ACM Symp. Theory Comput., 1986, pp. 136-146.
[9] V. M. Lo, "Heuristic algorithms for task assignment in distributed systems,"IEEE Trans. Comput., vol. C-37, pp. 1384-1397, Nov. 1988.
[10] D. M. Nicol, "Parallel algorithms for mapping pipelined and parallel computations," ICASE Rep. 88-2, NASA Contractor Rep. 181655, Apr. 1988.
[11] H. S. Stone, "Multiprocessor scheduling with the aid of network flow algorithms,"IEEE Trans. Software Eng., vol. SE-3, pp. 85-93, Jan. 1977.
[12] H. S. Stone, "Critical load factors in distributed computer systems,"IEEE Trans. Software Eng., vol. SE-4, pp. 254-258, May 1978.
[13] H. S. Stone and S. H. Bokhari, "Control of distributed processes,"IEEE Comput. Mag., vol. 11, pp. 97-106, July 1978.
[14] D. Towsley, "Allocating programs containing branches and loops within a multiple processor system,"IEEE Trans. Software Eng., vol. SE-12, pp. 1018-1024, Oct. 1986.

Index Terms:
optimal task assignment; linear array networks; distributed computing system; communication costs; NP-complete; network flow approach; task assignment; two-terminal network flow problem; computational complexity; computer networks; distributed processing.
Citation:
Cheol-Hoon Lee, Dongmyun Lee, Myunghwan Kim, "Optimal Task Assignment in Linear Array Networks," IEEE Transactions on Computers, vol. 41, no. 7, pp. 877-880, July 1992, doi:10.1109/12.256461
Usage of this product signifies your acceptance of the Terms of Use.