Online competitive algorithms for maximizing weighted throughput of unit jobs

Yair Bartal, Francis Y.L. Chin, Marek Chrobak, Stanley P.Y. Fung, Wojciech Jawor, Ron Lavi, Jir̂í Sgall, Tomáŝ Tichy

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

38 Scopus citations

Abstract

We study an online scheduling problem for unit-length jobs, where each job is specified by its release time, deadline, and a nonnegative weight. The goal is to maximize the weighted throughput, that is the total weight of scheduled jobs. We first give a randomized algorithm RMix with competitive ratio of e/(e -1) ≈1.582. Then we consider s-bounded instances where the span of each job is at most s. We give a 1.25-competitive randomized algorithm for 2-bounded instances, and a deterministic algorithm EDFα, whose competitive ratio on s-bounded instances is at most 2 -2/s + o(l/s). For 3-bounded instances its ratio is φ≈ 1.618, matching the lower bound. We also consider 2-uniform instances, where the span of each job is 2. We prove a lower bounds for randomized algorithms and deterministic memoryless algorithms. Finally, we consider the multiprocessor case and give an 1/(1 -(m/m+1) M)-competitive algorithm for M processors. We also show improved lower bounds for the general and 2-uniform cases.

Original languageAmerican English
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsVolker Diekert, Michel Habib
PublisherSpringer Verlag
Pages187-198
Number of pages12
ISBN (Print)9783540212362
DOIs
StatePublished - 2004

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2996
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

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