Bridging gap between standard and differential polynomial approxiamtion: the case of bin-packing

Marc Demange (1, 2) , Jérôme Monnot (3) , Vangelis. Paschos (3)

1 CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique
2 ESSEC Business School
3 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

The purpose of this paper is to mainly prove the following theorem: for every polynomial time algorithm running in time T(n) and guaranteeing standard-approximation ratio p for bin-packing, there exists an algorithm running in time O(nT(n)) and achieving differential-approximation ratio 2 - p for BP. This theorem has two main impacts. The first one is operational, deriving a polynomial time differential-approximation schema for bin-packing. The second one is structural, establishing a kind of reduction (to our knowledge not existing until now) between standard approximation and differential one.

Mots clés: Approximate algorithms; Differential ratio; Performance ratio; Analysis of Algorithms; Reductions

Domaines: Mathématiques générales [math.GM]; Complexité [cs.CC]; Algorithme et structure de données [cs.DS]; Mathématique discrète [cs.DM]

Marc Demange, Jérôme Monnot, Vangelis. Paschos. Bridging gap between standard and differential polynomial approxiamtion: the case of bin-packing. Applied Mathematics Letters, 1999, 12, pp.127-133. ⟨hal-00004007⟩