All-norm approximation algorithms

Yossi Azar, Leah Epstein, Yossi Richter, Gerhard J. Woeginger

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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 ρ-approximation algorithm, which supplies one solution that guarantees ρ-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 is associatedwith 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. [12] showeda 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 restrictedassignment 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 fixedn umber of machines.

Original languageEnglish
Title of host publicationAlgorithm Theory - SWAT 2002 - 8th Scandinavian Workshop on Algorithm Theory, Proceedings
EditorsMartti Penttonen, Erik Meineche Schmidt
PublisherSpringer Verlag
Number of pages10
ISBN (Print)9783540438663
StatePublished - 2002
Externally publishedYes
Event8th Scandinavian Workshop on Algorithm Theory, SWAT 2002 - Turku, Finland
Duration: 3 Jul 20025 Jul 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference8th Scandinavian Workshop on Algorithm Theory, SWAT 2002

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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