This Article 
 Bibliographic References 
 Add to: 
Graph Partitioning Using Learning Automata
February 1996 (vol. 45 no. 2)
pp. 195-208

Abstract—Given a graph G, we intend to partition its nodes into two sets of equal size so as to minimize the sum of the cost of the edges having end-points in different sets. This problem, called the uniform graph partitioning problem, is known to be NP-Complete. In this paper we propose the first reported learning-automaton based solution to the problem. We compare this new solution to various reported schemes such as the Kernighan-Lin's algorithm, and two excellent recent heuristic methods proposed by Rolland et al.—an extended local search algorithm and a genetic algorithm. The current automaton-based algorithm outperforms all the other schemes. We believe that it is the fastest algorithm reported to date. Additionally, our solution can also be adapted for the GPP (See note at end of Section 1) in which the edge costs are not constant but random variables whose distributions are unknown.

[1] E.H.L. Aarts and J.H.M. Korst, Simulated Annealing and Boltzmann Machines. John Wiley&Sons, 1989.
[2] L.A. Cox, Jr., L. Davis, and Y. Qiu, "Dynamic anticipatory routing in circuit-switched telecommunications networks," Handbook of Genetic Algorithms, L. Davis, ed. New York: Van Nostrand Reinhold, 1991.
[3] K.A. De Jong and W.M. Spears,“Using genetic algorithms to solve NP-complete problems,” Proc. 3rd Intl. Conf. on Genetic Algorithms, Morgan Kaufmann Publishers, pp. 124-132, June4-7, 1989.
[4] T.A. Feo and M. Khellaf, "A class of bounded approximation algorithms for graph partitioning," Networks, vol. 20, pp. 181-195, 1990.
[5] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness.New York: W.H. Freeman, 1979.
[6] M.R. Garey, D.S. Johnson, and L. Stockmeyer, "Some simplified NP-complete graph problems," Theor. Comput. Sci., vol. 1, pp. 237-267, 1976.
[7] D.E. Goldberg, "Computer-aided pipeline operation using genetic algorithms and rule learning. Part 1: Genetic algorithms in pipeline optimization," Eng. with Computers, vol. 3, pp. 35-45, 1987.
[8] D.E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning. Reading, Mass.: Addison-Wesley, 1989.
[9] B.L. Golden and C.C. Skiscim, "Using simulated annealing to solve routing and location problems," Naval Research Logistics Quarterly, vol. 33, pp. 261-279, 1986.
[10] D.S. Johnson, C. Aragon, L. McGeoch, and C. Schevon, "Optimization by Simulated Annealing: An Experimental Evaluation, Part 1, Graph Partitioning," Operations Research, vol. 37, pp. 865-892, 1989.
[11] B.W. Kernighan and S. Lin, "An efficient heuristic procedure for partitioning graphs." The Bell Systems Tech. J., vol. 49, pp. 291-307, 1970.
[12] M. Laguna, T.A. Feo, and H.C. Elrod, "A greedy adaptive search procedure for the two-paartition problem," Operations Research, vol. 42, pp. 677-687, 1994.
[13] G.E. Liepins and M.R. Hilliard, "Genetic algorithms: Foundations and applications," Annals of Operations Research, vol. 21, pp. 31-58, 1989.
[14] N.J. Nilsson, Principles of Artificial Intelligence. Morgan Kaufmann, 1980.
[15] K.S. Narendra and M.L. Thathachar, Learning Automata: An Introduction. Prentice Hall, 1989.
[16] B.J. Oommen and T. De St. Croix, "String taxonomy using object migrating automata," to appear IEEE Trans. Systems, Man, and Cybernetics.
[17] B.J. Oommen and C. Fothergill, "Fast learning automaton-based image examination and retrieval," The Computer J., vol. 36, no. 6, pp. 542-553, 1993.
[18] B.J. Oommen and D.C.Y. Ma, “Deterministic Learning Automata Solutions to the Equi-Partitioning Problem,” IEEE Trans. Computers, vol. 37, no. 1, pp. 2-14, Jan. 1988.
[19] B.J. Oommen, R.S. Valiveti, and J. Zgierski, "An adaptive learning solution to the keyboard optimization problem," IEEE Trans. Systems, Man, and Cybernetics, vol. 22, pp. 1,233-1243, Sept./Oct. 1992.
[20] B.J. Oommen and J. Zgierski, "A learning automaton solution to breaking substitution ciphers," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 15, pp. 185-192, Feb. 1993.
[21] H. Pirkul and E. Rolland, "New heuristic solution procedures for the uniform graph partitioning problem: Extensions and evaluation." Computers and Operations Research, Oct. 1994.
[22] E. Rolland, "Abstract heuristic search methods for graph partitioning," PhD dissertation, The Ohio State Univ., Columbus, 1991.
[23] E. Rolland and H. Pirkul, "Heuristic solution procedures for the graph partitioning problem," Proc. 1992 ORSA-CSTS Conf. Computer Science and Operations Research: New Developments in Their Interfaces,Williamsburg, pp. 475-490, 1992.
[24] E. Rolland, H. Pirkul, and F. Glover, "Tabu search for graph partitioning," to appear Annals of Operations Research (Special Issue on Meta-Heuristics).
[25] M.L. Tsetlin, "Automaton theory and the modeling of biological systems.New York and London: Academic, 1973.
[26] C.T. Yu, M.D. Siu, D. Lam, and T. Tai, "Adaptive clustering schemes: General framework," Proc. IEEE COMPSAC Conf., pp. 81-89, 1981.

Index Terms:
Heuristic search; graph partitioning; adaptive learning; learning automata.
B. John Oommen, Edward V. de St. Croix, "Graph Partitioning Using Learning Automata," IEEE Transactions on Computers, vol. 45, no. 2, pp. 195-208, Feb. 1996, doi:10.1109/12.485372
Usage of this product signifies your acceptance of the Terms of Use.