Bridging gap between standard and differential polynomial approximation: The case of bin-packing

The purpose of this paper is mainly to prove the following theorem: for eve ry polynomial time algorithm running in time T(n) and guaranteeing standard -approximation ratio rho for bin-packing, there exists an algorithm running in time O(nT(n)) and achieving differential-approximation ratio 2 - rho fo r BP. This theorem has two main impacts. The first one is "operational", de riving a polynomial time differential-approximation schema for bin-packing. The second one is structural, establishing a kind of reduction (to our kno wledge not existing until now) between standard approximation and different ial one. (C) 1999 Elsevier Science Ltd. All rights reserved.