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Main Title: The Power of α-Points in Preemptive Single Machine Scheduling
Author(s): Schulz, Andreas S.
Skutella, Martin
Type: Research Paper
Abstract: We consider the NP-hard preemptive single machine scheduling problem to minimize the total weighted completion time subject to release dates. A natural extension of Smith's ratio rule is to preempt the currently active job whenever a new job arrives that has higher ratio of weight to processing time. We prove that the competitive ratio of this simple on-line algorithm is precisely~2. We also show that list scheduling in order of random α-points drawn from the same schedule results in an on-line algorithm with competitive ratio~4/3. Since its analysis relies on a well-known integer programming relaxation of the scheduling problem, the relaxation has performance guarantee~4/3 as well. On the other hand, we show that it is at best an~8/7-relaxation.
Subject(s): scheduling theory
approximation algorithm
on-line algorithm
randomized algorithm
LP relaxation
combinatorial optimization
Issue Date: 1999
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 90C27 Combinatorial optimization
68Q25 Analysis of algorithms and problem complexity
90B35 Scheduling theory, deterministic
68M20 Performance evaluation; queueing; scheduling
90C59 Approximation methods and heuristics
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 1999, 639
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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