All-norm approximation algorithms

  • Authors:

  • Yossi Azar;Leah Epstein;Yossi Richter;Gerhard J. Woeginger

  • Affiliations:

  • School of Computer Science, Tel-Aviv University, Tel-Aviv, 69978, Israel;School of Computer Science, The Interdisciplinary Center, P.O. Box 167, 46150 Herzliya, Israel;School of Computer Science, Tel-Aviv University, Tel-Aviv, 69978, Israel;Department of Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands and Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, A ...

  • Venue:
  • Journal of Algorithms
  • Year:
  • 2004

Quantified Score

Hi-index 0.00

Visualization

Abstract

A major drawback in optimization problems and in particular in scheduling problems is that for every measure there may be a different optimal solution. In many cases the various measures are different lp norms. We address this problem by introducing the concept of an all-norm p-approximation algorithm, which supplies one solution that guarantees p-approximation to all lp norms simultaneously. Specifically, we consider the problem of scheduling in the restricted assignment model, where there are m machines and n jobs, each job is associated with a subset of the machines and should be assigned to one of them. Previous work considered approximation algorithms for each norm separately. Lenstra et al. [Math. Program. 46 (1990) 259-271] showed a 2-approximation algorithm for the problem with respect to the l∞ norm. For any fixed lp norm the previously known approximation algorithm has a performance of θ(p). We provide an all-norm 2-approximation polynomial algorithm for the restricted assignment problem. On the other hand, we show that for any given lp norm (p 1) there is no PTAS unless P=NP by showing an APX-hardness result. We also show for any given lp norm a FPTAS for any fixed number of machines.