A Distributed Algorithm for Max Independent Set Problem Based on Hopfield Networks
A distributed algorithm to find a maximal independent set of an undirected graph is proposed. It is borrowed by a centralized one and it is based on a sequence of Hopfield neural networks. We refer to the synchronous model of distributed computation in which the topology is described by the graph. We give an upper bound on the number of messages sent during the entire process of computation.
To test the algorithm we experimentally compare it with a probabilistic heuristic derived by Ant Colony Optimization technique and with the standard greedy algorithm.
KeywordsMax Independent Set Hopfield networks synchronous distributed algorithms
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- T. Bäck and S. Khuri. An evolutionary heuristic for the maximum independent set problem. In Z. Michalewicz, J. D. Schaffer, H. P. Schwefel, D. B. Fogel, and H. Kitano, editors, Proc. First IEEE Conf. Evolutionary Computation, IEEE World Congress on Computational Intelligence, volume 2, pages 531–535, Orlando FL, June 27–29, 1994. IEEE Press, Piscataway NJ.CrossRefGoogle Scholar
- U. Feige, S. Goldwasser, S. Safra L. Lovász, and M. Szegedy. Approximating clique is almost NP-complete. In Proceedings of the 32nd Annual IEEE Symposium on the Foundations of Computer Science, pages 2–12, 1991.Google Scholar
- T. A. Feo, M. G. C. Resende, and S.H. Smith. Greedy randomized adaptive search procedure for maximum independent set. Operations Research, 41, 1993.Google Scholar
- J. Håstad. Clique is hard to approximate within n 1e. In Proc. of the 37rd Annual IEEE Symposium on the Foundations of Computer Science, pages 627–636. IEEE, 1996.Google Scholar
- R.M. Karp. Reducibility among Combinatorial Problems, pages 85–103. Complexity of Computer Computations. Plenum Press, New York, 1972.Google Scholar
- G. Leguizamón, Z. Michalewicz, and M. Schütz. An ant system for the maximum independent set problem. In Proceedings of VII Argentine Congress of Computer Science (CACIC 2001), 2001.Google Scholar
- C.H. Papadimitriou. Computational Complexity. Addison-Wesley, 1994.Google Scholar