All-Norm Approximation Algorithms

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

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

5 Citations (Scopus)

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 ℓ p 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 ℓ p norms simultaneously. Specifically, we consider the problem of scheduling in the restricted assignment model, where there are m machines and n jobs, each 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. [12] showed a 2-approximation algorithm for the problem with respect to the ℓ∞ norm. For any fixed ℓ p 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 l p norm (p > 1) there is no PTAS unless P=NP by showing an APX-hardness result. We also show for any given ℓ p norm a FPTAS for any fixed number of machines.
Original languageEnglish
Title of host publicationAlgorithm Theory — SWAT 2002
Subtitle of host publication8th Scandinavian Workshop on Algorithm Theory Turku, Finland, July 3–5, 2002 Proceedings
EditorsMartti Penttonen, Erik Meineche Schmidt
Place of PublicationBerlin
PublisherSpringer
Pages288-297
ISBN (Electronic)978-3-540-45471-7
ISBN (Print)978-3-540-43866-3
DOIs
Publication statusPublished - 2002
Event8th Scandinavian Workshop on Algorithm Theory, SWAT 2002 - Turku, Finland
Duration: 3 Jul 20025 Jul 2002
Conference number: 8

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume2368
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Workshop

Workshop8th Scandinavian Workshop on Algorithm Theory, SWAT 2002
Abbreviated titleSWAT 2002
CountryFinland
CityTurku
Period3/07/025/07/02

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