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Deterministic Learning Automata Solutions to the Equipartitioning Problem
January 1988 (vol. 37 no. 1)
pp. 2-13
Three deterministic learning automata solutions to the problem of equipartitioning are presented. Although the first two are epsilon -optimal, they seem to be practically feasible only when a set of W objects is small. The last solution, which uses a novel learning automaton, demonstrates an excellent partitioning capability. Experimentally, this solution converges an order of magnitude faster

[1] D. M. Arnow and A. M. Tenenbaum, "An investigation of the move-ahead-k-rules," inCongressus Numerantium, Proc. Thirteenth Southeastern Conf. Combinatorics, Graph Theory Comput., Florida, Feb. 1982, pp. 47-65.
[2] J. R. Bitner, "Heuristics that dynamically organize data structures,"SIAM J. Comput., vol. 8, pp. 82-110, 1979.
[3] G. H. Gonnet, J. I. Munro, and H. Suwanda, "Exegesis of self organizing linear search,"SIAM J. Comput., vol. 10, pp. 613-637, 1981.
[4] M. Hammer and B. Niamir, "A heuristic approach to attribute partitioning," inProc. ACM SIGMOD Conf., 1979, pp. 93-101.
[5] M. Hammer and A. Chan, "Index selection in a self-adaptive database management system," inProc. 1976 ACM-SIGMOD Conf.(Washington, DC).
[6] W. J. Hendricks, "An account of self-organizing systems,"SIAM J. Comput., vol. 5, pp. 715-723, 1976.
[7] Y. C. Kan and S. M. Ross, "Optimal list order under partial memory constraints,"J. Appl. Probability, vol. 17, pp. 1004-1015, 1980.
[8] D. E. Knuth,The Art of Computer Programming, Vol. 3, Reading, MA: Addison-Wesley, 1973.
[9] S. Lakshmivarahan and M. A. L. Thathachar, "Absolutely expedient algorithms for stochastic automata,"IEEE Trans. Syst., Man, Cybern., vol. SMC-3, pp. 281-286, 1973.
[10] S. Lakshmivarahan,Learning Algorithms Theory and Applications, New York: Springer-Verlag, 1981.
[11] K. Lam and C. T. Yu, "A clustered search algorithm incorporating arbitrary term dependencies," Dep. Inform. Eng., Univ. Illinois, Chicago Circle, 1978.
[12] K. Lam and C. T. Yu, "An approximation algorithm for a file allocation problem in a hierarchical distributed system," inProc. ACM SIGMOD Conf., 1980, pp. 125-132.
[13] J. McCabe, "On serial files with relocatable records,"Oper. Res., vol. 12, pp. 609-618, 1965.
[14] K. S. Narendra and M. A. L. Thathachar, "Learning automata--A survey,"IEEE Trans. Syst., Man, Cybern., vol. SMC-4, pp. 323- 334, 1974.
[15] K. S. Narendra and M. A. L. Thathachar, "On the behavior of a learning automaton in a changing environment with routing applications,"IEEE Trans. Syst., Man, Cybern., vol. SMC-10, pp. 262-269, 1980.
[16] K. S. Narendra, E. Wright, and L. G. Mason, "Application of learning automata to telephone traffic routing,"IEEE Trans. Syst., Man, Cybern., vol. SMC-7, pp. 785-792, 1977.
[17] B. J. Oommen and E. R. Hansen, "The asymptotic optimality of two action discretized linear reward-inaction learning automata,"IEEE Trans. Syst., Man, Cybern., pp. 542-545, May/June 1984.
[18] B. J. Oommen, "Absorbing and ergodic discretized two action learning automata,"IEEE Trans. Syst., Man, Cybern., pp. 282-293, 1986.
[19] B. J. Oommen, "On the use of smoothsort and stochastic move-to-front operations for optimal list organization," inProc. Twenty-Second Allerton Conf., Oct. 1984, Urbana, IL, pp. 243-252.
[20] B. J. Oommen and E. R. Hansen, "List organizing strategies using stochastic move-to-front and stochastic move-to-rear operations,"Siam J. Comput., vol. 16, pp. 705-716, 1987.
[21] R. L. Rivest, "On self organizing sequential search heuristics,"Comm. Ass. Comput. Mach., vol. 19, pp. 63-67, 1976.
[22] D. Sleator and R. Tarjan, "Amortized efficiency of list update rules," inProc. Sixteenth Annu. ACM Symp. Theory of Comput., Apr. 1984, pp. 488-492.
[23] G. Salton,Dynamic Information and Library Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.
[24] M. Schkolnick, "A clustering algorithm for hierarchical structures,"ACM Trans. Database Syst., 1977, pp. 27-44.
[25] M. L. Tsetlin, "On the behavior of finite automata in random media,"Automat. Telemek., vol. 22, pp. 1345-1354, 1961.
[26] M. L. Tsetlin,Automaton Theory and Modelling of Biological Systems. New York: Academic, 1973.
[27] C. J. Van Rijsbergen, "A theoretical basis for the use of co-occurrence data in information retrieval,"J. Documentation, pp. 106-119, 1977.
[28] C. T. Yu and G. Salton, "Precision weighting--An effective automatic indexing method,"J. Ass. Comput. Mach., pp. 76-78, 1976.
[29] C. T. Yu, M. K. Siu, K. Lam, and M. Ozsoyoglu, "Performance analysis of three related assignment problems," inProc. ACM SIGMOD Conf., May 1979.
[30] C. T. Yu, M. K. Siu, K. Lam, and F. Tai, "Adaptive clustering schemes: General framework," inProc. IEEE COMPSAC Conf., 1981, pp. 81-89.
[31] D. C. Y. Ma, "Object partitioning by using learning automata," M.C.S. Thesis, School Comput. Sci., Carleton Univ., Ottawa, Canada, Apr. 1986.

Index Terms:
convergence rate; epsilon -optimal solutions; equipartitioning problem; deterministic learning automata solutions; deterministic automata; learning systems; set theory.
B.J. Oommen, D.C.Y. Ma, "Deterministic Learning Automata Solutions to the Equipartitioning Problem," IEEE Transactions on Computers, vol. 37, no. 1, pp. 2-13, Jan. 1988, doi:10.1109/12.75146
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