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Allocating Modules to Processors in a Distributed System
November 1989 (vol. 15 no. 11)
pp. 1427-1436

The author studies the complexity of the problem of allocating modules to processes in a distributed system to minimize total communication and execution costs. He shows that unless P=NP, there can be no polynomial-time epsilon -approximate algorithm for the problem, nor can there exist a local search algorithm that requires polynomial time per iteration and yields an optimum assignment. Both results hold even if the communication graph is planar and bipartite. On the positive side, it is shown that if the communication graph is a partial k-tree or an almost-tree with parameter k, the module allocation problem can be solved in polynomial time.

[1] S. Arnborg, "Efficient algorithms for combinatorial problems on graphs with bounded decomposability--A survey,"BIT, vol. 25, pp. 305-314, 1985.
[2] S. Arnborg, D. G. Corneil, and A. Proskurowski, "Complexity of finding embeddings in ak-tree,"SIAM J. Algebraic and Discrete Methods, vol. 8, no. 2, 1987, pp. 277-284.
[3] A. V. Aho, J. E. Hopcroft, and J. D. Ullman,The Design and Analysis of Computer Algorithms. Menlo Park, CA: Addison-Wesley, 1974.
[4] S. Arnborg and A. Proskurowski, "Characterization and recognition of partial 3-trees,"SIAM J. Alg. Discr. Methods, vol. 7, pp. 305- 314, 1986.
[5] S. Arnborg and A. Proskurowski, "Linear-time algorithms for NP-hard problems restricted to partialk-trees," manuscript.
[6] H. L. Bodlaender, "Classes of graphs with bounded tree-width," Dep. Comput. Sci., Univ. Utrecht, The Netherlands, Tech. Rep. RUU-CS-86-22, Dec. 1986.
[7] H. L. Bodlaender, "Some classes of graphs with bounded tree-width,"Bull. EATCS, vol. 36, pp. 116-126, 1988.
[8] S. Bokhari, "A shortest tree algorithm for optimal assignments across space and time in a distributed processor system,"IEEE Trans. Software Eng., vol. SE-7, no. 6, pp. 583-589, 1981.
[9] U. Bertelèand F. Brioschi,Nonserial Dynamic Programming. New York: Academic, 1972.
[10] W. W. Chu, L. J. Holloway, M. Lan, and K. Efe, "Task allocation in distributed data processing,"Computer, pp. 57-69, Nov. 1980.
[11] E. S. Elmallah and C. J. Colbourn, "Reliability ofΔ-Ynetworks,"Congressus Numerantium, vol. 48, pp. 49-54, 1985.
[12] S. Even, A. Itai, and A. Shamir, "On the complexity of multicommodity flow problems,"SIAM J. Comput., vol. 5, no. 4, pp. 691- 703, 1976.
[13] D. Fernández-Baca and G. Slutzki, "Solving parametric problems on trees," Dep. Comput. Sci., Iowa State Univ., Tech. Rep. 87-12, 1987, to appear inJ. Algorithms.
[14] M. R. Garey and D. S. Johnson,Computers and Intractability: A Guide to Theory of NP-Completeness. San Francisco, CA: Freeman, 1979.
[15] Y. Gurevich, L. Stockmeyer, and U. Vishkin, "Solving NP-hard problems on graphs that are almost trees and an application to facility location problems,"J. ACM, vol. 31, no. 3, pp. 459-473, 1984.
[16] D. Gusfield, "Parametric combinatorial computing and a problem of module distribution,"J. ACM, no. 3, pp. 551-563, 1983.
[17] D. Lichtenstein, "Planar formulae and their uses,"SIAM J. Comput., vol. 11, no. 2, pp. 329-343, 1982.
[18] V. M. Lo, "Heuristic algorithms for task assignment in distributed systems,"IEEE Trans. Comput., vol. C-37, no. 11, pp. 1384-1397, 1988.
[19] R. Lipton and R. Tarjan, "Applications of a planar separator theorem,"SIAM J. Comput., vol. 9, no. 3, pp. 615-627, 1980.
[20] C. H. Papadimitriou and K. Steiglitz, "The complexity of local search for the traveling salesman problem,"SIAM J. Comput., vol. 6, no. 1, pp. 76-83, 1977.
[21] C. H. Papadimitriou and K. Steiglitz,Combinatorial Optimization: Algorithms and Complexity. Englewood Cliffs, NJ: Prentice-Hall, 1982.
[22] A. Rosenthal, "Dynamic programming is optimal for nonserial optimization problems,"SIAM J. Comput., vol. 11, no. 1, pp. 47-59, 1982.
[23] N. Robertson and P. D. Seymour, "Graph minors XIII: The disjoint paths problem," Manuscript, Sept. 1986.
[24] J. B. Sinclair, "Efficient computation of optimal assignments for distributed tasks,"J. Parallel Distributed Comput., vol. 4, pp. 342-362, 1987.
[25] H. Stone, "Multiprocessor scheduling with the aid of network flow algorithms,"IEEE Trans. Software Eng., vol. SE-3, pp. 85-94, 1977.
[26] H. Stone, "Critical load factors in two-processor distributed systems,"IEEE Trans. Software Eng., vol. SE-4, pp. 254-258, 1978.
[27] S. Sahni and T. Gonzalez, "P-complete approximation problems,"J. ACM, vol. 23, pp. 55-565, 1976.
[28] 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:
distributed system; complexity; execution costs; P=NP; polynomial-time epsilon -approximate algorithm; local search algorithm; polynomial time; iteration; optimum assignment; communication graph; planar; bipartite; partial k-tree; almost-tree; module allocation problem; computational complexity; distributed processing; graph theory
Citation:
D. Fernandez-Baca, "Allocating Modules to Processors in a Distributed System," IEEE Transactions on Software Engineering, vol. 15, no. 11, pp. 1427-1436, Nov. 1989, doi:10.1109/32.41334
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