### 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 language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 862-874 |

Number of pages | 13 |

Volume | 2076 LNCS |

Publication status | Published - 2001 |

Event | 28th International Colloquium on Automata, Languages and Programming, ICALP 2001 - Crete, Greece Duration: Jul 8 2001 → Jul 12 2001 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2076 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 28th International Colloquium on Automata, Languages and Programming, ICALP 2001 |
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Country | Greece |

City | Crete |

Period | 7/8/01 → 7/12/01 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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.

}

TY - GEN

T1 - The buffer minimization problem for multiprocessor scheduling with conflicts

AU - Chrobak, Marek

AU - Csirik, J.

AU - Imreh, Csanád

AU - Noga, John

AU - Sgall, Jiří

AU - Woeginger, Gerhard J.

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84857732838&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84857732838&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84857732838

SN - 3540422870

SN - 9783540422877

VL - 2076 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 862

EP - 874

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -