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://www.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://www.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://www.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://www.numdam.org/articles/10.1051/ita:2006012/
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