We propose a heuristic for solving the maximum independent set problem for a set of processors in a network with arbitrary topology. We assume an asynchronous model of computation and we use modified Hopfield neural networks to find high quality solutions. We analyze the algorithm in terms of the number of rounds necessary to find admissible solutions both in the worst case (theoretical analysis) and in the average case (experimental Analysis). We show that our heuristic is better than the greedy one at 1% significance level.
Mots clés : max independent set, hopfield networks, asynchronous distributed algorithms
@article{ITA_2006__40_2_371_0,
author = {Grossi, Giuliano and Marchi, Massimo and Posenato, Roberto},
title = {Solving maximum independent set by asynchronous distributed hopfield-type neural networks},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {371--388},
publisher = {EDP-Sciences},
volume = {40},
number = {2},
year = {2006},
doi = {10.1051/ita:2006012},
mrnumber = {2252645},
zbl = {1112.68119},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ita:2006012/}
}
TY - JOUR AU - Grossi, Giuliano AU - Marchi, Massimo AU - Posenato, Roberto TI - Solving maximum independent set by asynchronous distributed hopfield-type neural networks JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2006 SP - 371 EP - 388 VL - 40 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita:2006012/ DO - 10.1051/ita:2006012 LA - en ID - ITA_2006__40_2_371_0 ER -
%0 Journal Article %A Grossi, Giuliano %A Marchi, Massimo %A Posenato, Roberto %T Solving maximum independent set by asynchronous distributed hopfield-type neural networks %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2006 %P 371-388 %V 40 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita:2006012/ %R 10.1051/ita:2006012 %G en %F ITA_2006__40_2_371_0
Grossi, Giuliano; Marchi, Massimo; Posenato, Roberto. Solving maximum independent set by asynchronous distributed hopfield-type neural networks. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 2, pp. 371-388. doi : 10.1051/ita:2006012. http://archive.numdam.org/articles/10.1051/ita:2006012/
[1] and, An evolutionary heuristic for the maximum independent set problem, in Proc. First IEEE Conf. Evolutionary Computation, IEEE World Congress on Computational Intelligence, edited by Z. Michalewicz, J.D. Schaffer, H.-P. Schwefel, D.B. Fogel and H. Kitano, Orlando FL, June 27-29. IEEE Press, Piscataway NJ 2 (1994) 531-535.
[2] , Finding a maximal weighted independent set in wireless networks. Telecommunication Systems, Special Issue on Mobile Computing and Wireless Networks 18 (2001) 155-168. | Zbl
[3] and, Reactive local search for the maximum clique problem. Algorithmica 29 (2001) 610-637. | Zbl
[4] , and, A neural algorithm for the maximum clique problem: Analysis, experiments and circuit implementation. Algoritmica 33 (2002) 71-88. | Zbl
[5] ,, and, Annealed replication: A new heuristic for the maximum clique problem. Discrete Appl. Math. 121 (2000) 27-49. | Zbl
[6] , and, Ant algorithms for discrete optimization. Artificial Life 5 (1996) 137-172.
[7] ,,, and, Approximating clique is almost NP-complete, in Proceedings of the 32nd Annual IEEE Symposium on the Foundations of Computer Science (1991) 2-12.
[8] , and, Greedy randomized adaptive search procedure for maximum independent set. Oper. Res. 41 (1993). | Zbl
[9] and, Multicluster, mobile, multimedia radio network. Wireless Networks 1 (1995) 255-265.
[10] ,, and, Self-stabilizing protocols for maximal matching and maximal independent sets for ad hoc networks, in Workshop on Advances in Parallel and Distributed Computational Models (2003).
[11] and, A distributed algorithm for max independent set problem based on Hopfield networks, in Neural Nets: 13th Italian Workshop on Neural Nets (WIRN 2002), edited by M. Marinaro and R. Tagliaferri. Springer-Verlag. Lect. Notes Comput. Sci. 2486 (2002) 64-74. | Zbl
[12] and, Greedy is good: Approximating independent sets in sparse and bounded-degree graphs. Algorithmica 18 (1997) 145-163. | Zbl
[13] , Clique is hard to approximate within , in Proc. of the 37rd Annual IEEE Symposium on the Foundations of Computer Science (1996) 627-636.
[14] , Neural networks and physical systems with emergent collective computational abilities, in Proceedings of the National Academy of Sciences of the United States of America 79 (1982) 2554-2558.
[15] and, An efficient fault-containing self-stabilizing algorithm for finding a maximal independent set. IEEE Transactions on Parallel and Distributed Systems 14 (2003) 742-754.
[16] and, Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge. DIMACS Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society (1996). | MR | Zbl
[17] , Reducibility among Combinatorial Problems. Complexity of Computer Computations. Plenum Press, New York (1972) 85-103.
[18] , and, An ant system for the maximum independent set problem, in Proceedings of VII Argentine Congress of Computer Science (CACIC 2001) (2001).
[19] , Improving convergence and solution quality of Hopfield-type neural networks with augmented Lagrange multipliers. IEEE Trans. Neural Networks 7 (1996) 1507-1516.
[20] , A simple heuristic based genetic algorithm for the maximum clique problem, in Proc. ACM Symp. Appl. Comput (1998) 366-373.
[21] , Computational Complexity. Addison-Wesley (1994). | MR | Zbl
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