The buffer minimization problem for multiprocessor scheduling with conflicts

Marek Chrobak, J. Csirik, Csanád Imreh, John Noga, Jiří Sgall, Gerhard J. Woeginger

Research output: Chapter in Book/Report/Conference proceedingConference contribution

20 Citations (Scopus)

Abstract

We consider the problem of scheduling a sequence of tasks in a multi-processor system with conflicts. Conflicting processors cannot process tasks at the same time. At certain times new tasks arrive in the system, where each task specifies the amount of work (processing time) added to each processor's workload. Each processor stores this workload in its input buffer. Our objective is to schedule task execution, obeying the conflict constraints, and minimizing the maximum buffer size of all processors. In the off-line case, we prove that, unless P = NP, the problem does not have a polynomial-time algorithm with a polynomial approximation ratio. In the on-line case, we provide the following results: (i) a competitive algorithm for general graphs, (ii) tight bounds on the competitive ratios for cliques and complete k-partite graphs, and (iii) a (δ=2 + 1)-competitive algorithm for trees, where δ is the diameter. We also provide some results for small graphs with up to 4 vertices.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages862-874
Number of pages13
Volume2076 LNCS
Publication statusPublished - 2001
Event28th International Colloquium on Automata, Languages and Programming, ICALP 2001 - Crete, Greece
Duration: Jul 8 2001Jul 12 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2076 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other28th International Colloquium on Automata, Languages and Programming, ICALP 2001
CountryGreece
CityCrete
Period7/8/017/12/01

Fingerprint

Multiprocessor Scheduling
Minimization Problem
Buffer
Scheduling
Workload
Graph in graph theory
Polynomial approximation
Competitive Ratio
Multiprocessor Systems
Polynomial Approximation
Clique
Polynomial-time Algorithm
Schedule
Polynomials
Line
Processing
Conflict

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Chrobak, M., Csirik, J., Imreh, C., Noga, J., Sgall, J., & Woeginger, G. J. (2001). The buffer minimization problem for multiprocessor scheduling with conflicts. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2076 LNCS, pp. 862-874). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2076 LNCS).

The buffer minimization problem for multiprocessor scheduling with conflicts. / Chrobak, Marek; Csirik, J.; Imreh, Csanád; Noga, John; Sgall, Jiří; Woeginger, Gerhard J.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2076 LNCS 2001. p. 862-874 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2076 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Chrobak, M, Csirik, J, Imreh, C, Noga, J, Sgall, J & Woeginger, GJ 2001, The buffer minimization problem for multiprocessor scheduling with conflicts. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 2076 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2076 LNCS, pp. 862-874, 28th International Colloquium on Automata, Languages and Programming, ICALP 2001, Crete, Greece, 7/8/01.
Chrobak M, Csirik J, Imreh C, Noga J, Sgall J, Woeginger GJ. The buffer minimization problem for multiprocessor scheduling with conflicts. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2076 LNCS. 2001. p. 862-874. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Chrobak, Marek ; Csirik, J. ; Imreh, Csanád ; Noga, John ; Sgall, Jiří ; Woeginger, Gerhard J. / The buffer minimization problem for multiprocessor scheduling with conflicts. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2076 LNCS 2001. pp. 862-874 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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