The Probabilistic Minimum Coloring Problem (Preliminary version)
نویسندگان
چکیده
Nous étudions le problème de coloration probabiliste (PCOLOR) sous une stratégie de modification consistant, pour une solution a priori C , de supprimer les sommets qui son absents de C . Nous calculons la fonction objectif associée avec cette stratégie, donnons des bornes pour sa valeur et caractérisons la complexité algorithmique du calcul de la solution a priori optimal. Nous démontrons que PCOLOR est NP-difficile et nous concevons an algorithme polynomial approché qui garantit un rapport non-trivial. Nous démontrons ensuite que, même dans les graphes bipartis, le problème reste NP-difficile et que la 2-coloration unique d’un tel graphe est une approximation à rapport constant. Enfin nous prouvons que PCOLOR est polynomial dans les compléments des graphes bipartis.
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