Precedence-constrained scheduling problems parameterized by partial order width

René van Bevern; Robert Bredereck; Laurent Bulteau; Christian Komusiewicz; Nimrod Talmon; Gerhard J. Woeginger

doi:10.1007/978-3-319-44914-2_9

Precedence-constrained scheduling problems parameterized by partial order width

René van Bevern, Robert Bredereck, Laurent Bulteau, Christian Komusiewicz, Nimrod Talmon, Gerhard J. Woeginger

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

Abstract

Negatively answering a question posed by Mnich and Wiese (Math. Program. 154(1–2):533–562), we show that P2|prec, p_j∈{1, 2}|C_max, the problem of finding a non-preemptive minimummakespan schedule for precedence-constrained jobs of lengths 1 and 2 on two parallel identical machines, is W[2]-hard parameterized by the width of the partial order giving the precedence constraints. To this end, we show that Shuffle Product, the problem of deciding whether a given word can be obtained by interleaving the letters of k other given words, is W[2]-hard parameterized by k, thus additionally answering a question posed by Rizzi and Vialette (CSR 2013). Finally, refining a geometric algorithm due to Servakh (Diskretn. Anal. Issled. Oper. 7(1):75–82), we show that the more general Resource-Constrained Project Scheduling problem is fixed-parameter tractable parameterized by the partial order width combined with the maximum allowed difference between the earliest possible and factual starting time of a job.

Original language	American English
Title of host publication	Discrete Optimization and Operations Research - 9th International Conference, DOOR 2016, Proceedings
Editors	Michael Khachay, Panos Pardalos, Yury Kochetov, Vladimir Beresnev, Evgeni Nurminski
Publisher	Springer Verlag
Pages	105-120
Number of pages	16
ISBN (Print)	9783319449135
DOIs	https://doi.org/10.1007/978-3-319-44914-2_9
State	Published - 1 Jan 2016
Externally published	Yes
Event	9th International Conference on Discrete Optimization and Operations Research, DOOR 2016 - Vladivostok, Russian Federation Duration: 19 Sep 2016 → 23 Sep 2016

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9869 LNCS

Conference

Conference	9th International Conference on Discrete Optimization and Operations Research, DOOR 2016
Country/Territory	Russian Federation
City	Vladivostok
Period	19/09/16 → 23/09/16

Keywords

Makespan minimization
Parallel identical machines
Parameterized complexity
Resource-constrained project scheduling
Shuffle product

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-319-44914-2_9

Cite this

van Bevern, R., Bredereck, R., Bulteau, L., Komusiewicz, C., Talmon, N., & Woeginger, G. J. (2016). Precedence-constrained scheduling problems parameterized by partial order width. In M. Khachay, P. Pardalos, Y. Kochetov, V. Beresnev, & E. Nurminski (Eds.), Discrete Optimization and Operations Research - 9th International Conference, DOOR 2016, Proceedings (pp. 105-120). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9869 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-44914-2_9

van Bevern, René ; Bredereck, Robert ; Bulteau, Laurent et al. / Precedence-constrained scheduling problems parameterized by partial order width. Discrete Optimization and Operations Research - 9th International Conference, DOOR 2016, Proceedings. editor / Michael Khachay ; Panos Pardalos ; Yury Kochetov ; Vladimir Beresnev ; Evgeni Nurminski. Springer Verlag, 2016. pp. 105-120 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Precedence-constrained scheduling problems parameterized by partial order width",

abstract = "Negatively answering a question posed by Mnich and Wiese (Math. Program. 154(1–2):533–562), we show that P2|prec, pj∈{1, 2}|Cmax, the problem of finding a non-preemptive minimummakespan schedule for precedence-constrained jobs of lengths 1 and 2 on two parallel identical machines, is W[2]-hard parameterized by the width of the partial order giving the precedence constraints. To this end, we show that Shuffle Product, the problem of deciding whether a given word can be obtained by interleaving the letters of k other given words, is W[2]-hard parameterized by k, thus additionally answering a question posed by Rizzi and Vialette (CSR 2013). Finally, refining a geometric algorithm due to Servakh (Diskretn. Anal. Issled. Oper. 7(1):75–82), we show that the more general Resource-Constrained Project Scheduling problem is fixed-parameter tractable parameterized by the partial order width combined with the maximum allowed difference between the earliest possible and factual starting time of a job.",

keywords = "Makespan minimization, Parallel identical machines, Parameterized complexity, Resource-constrained project scheduling, Shuffle product",

author = "{van Bevern}, Ren{\'e} and Robert Bredereck and Laurent Bulteau and Christian Komusiewicz and Nimrod Talmon and Woeginger, {Gerhard J.}",

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van Bevern, R, Bredereck, R, Bulteau, L, Komusiewicz, C, Talmon, N & Woeginger, GJ 2016, Precedence-constrained scheduling problems parameterized by partial order width. in M Khachay, P Pardalos, Y Kochetov, V Beresnev & E Nurminski (eds), Discrete Optimization and Operations Research - 9th International Conference, DOOR 2016, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9869 LNCS, Springer Verlag, pp. 105-120, 9th International Conference on Discrete Optimization and Operations Research, DOOR 2016, Vladivostok, Russian Federation, 19/09/16. https://doi.org/10.1007/978-3-319-44914-2_9

Precedence-constrained scheduling problems parameterized by partial order width. / van Bevern, René; Bredereck, Robert; Bulteau, Laurent et al.
Discrete Optimization and Operations Research - 9th International Conference, DOOR 2016, Proceedings. ed. / Michael Khachay; Panos Pardalos; Yury Kochetov; Vladimir Beresnev; Evgeni Nurminski. Springer Verlag, 2016. p. 105-120 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9869 LNCS).

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

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AU - van Bevern, René

AU - Bredereck, Robert

AU - Bulteau, Laurent

AU - Komusiewicz, Christian

AU - Talmon, Nimrod

AU - Woeginger, Gerhard J.

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2016.

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Y1 - 2016/1/1

N2 - Negatively answering a question posed by Mnich and Wiese (Math. Program. 154(1–2):533–562), we show that P2|prec, pj∈{1, 2}|Cmax, the problem of finding a non-preemptive minimummakespan schedule for precedence-constrained jobs of lengths 1 and 2 on two parallel identical machines, is W[2]-hard parameterized by the width of the partial order giving the precedence constraints. To this end, we show that Shuffle Product, the problem of deciding whether a given word can be obtained by interleaving the letters of k other given words, is W[2]-hard parameterized by k, thus additionally answering a question posed by Rizzi and Vialette (CSR 2013). Finally, refining a geometric algorithm due to Servakh (Diskretn. Anal. Issled. Oper. 7(1):75–82), we show that the more general Resource-Constrained Project Scheduling problem is fixed-parameter tractable parameterized by the partial order width combined with the maximum allowed difference between the earliest possible and factual starting time of a job.

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van Bevern R, Bredereck R, Bulteau L, Komusiewicz C, Talmon N, Woeginger GJ. Precedence-constrained scheduling problems parameterized by partial order width. In Khachay M, Pardalos P, Kochetov Y, Beresnev V, Nurminski E, editors, Discrete Optimization and Operations Research - 9th International Conference, DOOR 2016, Proceedings. Springer Verlag. 2016. p. 105-120. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-44914-2_9

Precedence-constrained scheduling problems parameterized by partial order width

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Conference

Keywords

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