Apres un rappel des algorithmes gloutons, cet article presente deux methodes de resolution accelerees et exactes des problemes de recherche de sousensembles optimaux maximisant une fonction objectif surmodulaire: une premiere methode fournit de tres bonnes solutions approchees et un encadrement (au sens de l’inclusion) de l’optimum exact; une deuxieme methode de resolution exacte, de type enumeratif utilise comme solutions de depart celles donnees par la methode precedente. After a short survey of the greedy algorithms, this article introduces two accelerated and accurate methods to solve the problems of the research of a subset maximizing a supermodularobjective function: a first method leads to very good approximate solutions and gives lower and upper bounds (in the meaning of inclusion) of the optimal subset; a second enumerative method giving the exact solution uses as starting solutions, the ones given by the first method.