no. 2
Semi-definite positive programming relaxations for graph K 𝐧 -coloring in frequency assignment
RAIRO - Operations Research - Recherche Opérationnelle, Tome 35 (2001) no. 2, pp. 211-228

In this paper we will describe a new class of coloring problems, arising from military frequency assignment, where we want to minimize the number of distinct n-uples of colors used to color a given set of n-complete-subgraphs of a graph. We will propose two relaxations based on Semi-Definite Programming models for graph and hypergraph coloring, to approximate those (generally) NP-hard problems, as well as a generalization of the works of Karger et al. for hypergraph coloring, to find good feasible solutions with a probabilistic approach.

Dans cet article, nous décrivons une nouvelle classe de problèmes de coloration rencontrés en Allocation de Fréquences militaire : nous voulons minimiser le nombre de n-uplets distincts utilisés pour colorier un ensemble doné de n-cliques d’un graphe. Pour approcher ces problèmes généralement NP-difficiles, nous proposons deux relaxations basées sur les modélisations semi-définies de la coloration de graphes et d’hypergraphes, ainsi qu’une généralisation des travaux de Karger et al. à la coloration d’hypergraphes, pour trouver de bonnes solutions faisables par une approche probabiliste.

Keywords: discrete optimization, semidefinite programming, frequency assignment, graph coloring, hypergraph coloring 
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     author = {Meurdesoif, Philippe and Rottembourg, Beno{\^\i}t},
     title = {Semi-definite positive programming relaxations for graph $K_{\bf n}$-coloring in frequency assignment},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {211--228},
     year = {2001},
     publisher = {EDP Sciences},
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Meurdesoif, Philippe; Rottembourg, Benoît. Semi-definite positive programming relaxations for graph $K_{\bf n}$-coloring in frequency assignment. RAIRO - Operations Research - Recherche Opérationnelle, Tome 35 (2001) no. 2, pp. 211-228. https://www.numdam.org/item/RO_2001__35_2_211_0/

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