The Probabilistic Minimum Coloring Problem
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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