Minimizing average completion of dedicated tasks and interval graphs

Magnús M. Halldórsson; Guy Kortsarz; Hadas Shachnai

Minimizing average completion of dedicated tasks and interval graphs

Magnús M. Halldórsson, Guy Kortsarz, Hadas Shachnai

Computer Science

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

Abstract

Scheduling dependent jobs on multiple machines is modeled as a graph (multi)coloring problem. The focus of this work is on the sum of completion times measure. This is known as the sum (multi)coloring of the conflict graph. We also initiate the study of the waiting time and the robust throughput of colorings. For uniform-length tasks we give an algorithm which simultaneously approximates these two measures, as well as sum coloring and the chromatic number, within constant factor, for any graph in which the k-colorable subgraph problem is polynomially solvable. In particular, this improves the best approximation ratio known for sum coloring interval graphs from 2 to 1.665. We then consider the problem of scheduling non-preemptively tasks (of non-uniform lengths) that require exclusive use of dedicated processors. The objective is to minimize the sum of completion times. We obtain the first constant factor approximations for this problem, when each task uses a constant number of processors.

Original language	English
Title of host publication	Approximation, Randomization, and Combinatorial Optimization
Subtitle of host publication	Algorithms and Techniques - 4th International Workshop on Approximation, Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001, Proceedings
Editors	Luca Trevisan, Klaus Jansen, Michel Goemans, Jose D. P. Rolim
Publisher	Springer Verlag
Pages	114-126
Number of pages	13
ISBN (Electronic)	3540424709
State	Published - 2015
Event	4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001 - Berkeley, United States Duration: 18 Aug 2001 → 20 Aug 2001

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2129
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001
Country/Territory	United States
City	Berkeley
Period	18/08/01 → 20/08/01

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2001

Cite this

Halldórsson, M. M., Kortsarz, G., & Shachnai, H. (2015). Minimizing average completion of dedicated tasks and interval graphs. In L. Trevisan, K. Jansen, M. Goemans, & J. D. P. Rolim (Eds.), Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 4th International Workshop on Approximation, Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001, Proceedings (pp. 114-126). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2129). Springer Verlag.

Halldórsson, Magnús M. ; Kortsarz, Guy ; Shachnai, Hadas. / Minimizing average completion of dedicated tasks and interval graphs. Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 4th International Workshop on Approximation, Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001, Proceedings. editor / Luca Trevisan ; Klaus Jansen ; Michel Goemans ; Jose D. P. Rolim. Springer Verlag, 2015. pp. 114-126 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Halldórsson, MM, Kortsarz, G & Shachnai, H 2015, Minimizing average completion of dedicated tasks and interval graphs. in L Trevisan, K Jansen, M Goemans & JDP Rolim (eds), Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 4th International Workshop on Approximation, Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2129, Springer Verlag, pp. 114-126, 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001, Berkeley, United States, 18/08/01.

Minimizing average completion of dedicated tasks and interval graphs. / Halldórsson, Magnús M.; Kortsarz, Guy; Shachnai, Hadas.
Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 4th International Workshop on Approximation, Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001, Proceedings. ed. / Luca Trevisan; Klaus Jansen; Michel Goemans; Jose D. P. Rolim. Springer Verlag, 2015. p. 114-126 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2129).

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

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Halldórsson MM, Kortsarz G, Shachnai H. Minimizing average completion of dedicated tasks and interval graphs. In Trevisan L, Jansen K, Goemans M, Rolim JDP, editors, Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 4th International Workshop on Approximation, Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001, Proceedings. Springer Verlag. 2015. p. 114-126. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

Minimizing average completion of dedicated tasks and interval graphs

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