Weighted sum coloring in batch scheduling of conflicting jobs

Leah Epstein, Magnús M. Halldórsson, Asaf Levin, Hadas Shachnai

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

Abstract

Motivated by applications in batch scheduling of interval jobs, processes in manufacturing systems and distributed computing, we study two related problems. Given is a set of jobs {J1,. Jn}, where Jj has the processing time Pj, and an undirected intersection graph G = ({1, 2,., n}, E); there is an edge (i, j) φ E if the pair of jobs Ji and J j cannot be processed in the same batch. At any period of time, we can process a batch of jobs that forms an independent set in G. The batch completes its processing when the last job in the batch completes its execution. The goal is to minimize the sum of job completion times. Our two problems differ in the definition of completion time of a job within a given batch. In the first variant, a job completes its execution when its batch is completed, whereas in the second variant, a job completes execution when its own processing is completed. For the first variant, we show that an adaptation of the greedy set cover algorithm gives a 4-approximation for perfect graphs. For the second variant, we give new or improved approximations for a number of different classes of graphs. The algorithms are of widely different genres (LP, greedy, subgraph covering), yet they curiously share a common feature in their use of randomized geometric partitioning.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 a
PublisherSpringer Verlag
Pages116-127
Number of pages12
ISBN (Print)3540380442, 9783540380443
DOIs
StatePublished - 2006
Event9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 and 10th International Workshop on Randomization and Computation, RANDOM 2006 - Barcelona, Spain
Duration: 28 Aug 200630 Aug 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4110 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 and 10th International Workshop on Randomization and Computation, RANDOM 2006
Country/TerritorySpain
CityBarcelona
Period28/08/0630/08/06

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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