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No Free Lunch et recherche de solutions structurantes en coloration

Abstract : First we will introduce the No Free Lunch theorems by basing our arguments on D. H. Wolpert and W.G. Macready's articles (1997 EEEI version) but also on the numerous reactions those results produced in the community of optimization. As the global approach to the problems and the necessity of searching for general characteristics appeared to us as the most logical point to focus on, we will then attempt to make use of this method for simple and non oriented graphs. This field has been chosen because first it was a very interesting case to study and then because of its ability at multiplying in the numerous problems of optimization. We will bring up the notion of a graph's decomposition into maximal cliques as well as the constructive series' one which is able to reconstruct a graph from its primary cliques- as prime numbers would for natural numbers. Next we will produce a main algorithm and we will study two peculiar cases which, altogether, supply a partition of a set the studied graph's proper coloring. Then we will find the chromatic polynomial through a formal way, regardless of the number of available colours. We will draw up a Galois connection between fitted coloring and subgraphs generated by embedded families of maximal cliques provided that they are the whole decomposition of growing subgraphs from the entire graph.
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Submitted on : Friday, July 8, 2011 - 11:17:59 PM
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Jean-Noel Martin. No Free Lunch et recherche de solutions structurantes en coloration. Modélisation et simulation. Université de Technologie de Belfort-Montbeliard, 2010. Français. ⟨NNT : 2010BELF0147⟩. ⟨tel-00607481⟩

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