Scheduling two competing agents when one agent has significantly fewer jobs

Dan Hermelin; Judith Madeleine Kubitza; Dvir Shabtay; Nimrod Talmon; Gerhard Woeginger

doi:https://doi.org/10.4230/LIPIcs.IPEC.2015.55

Scheduling two competing agents when one agent has significantly fewer jobs

Dan Hermelin, Judith Madeleine Kubitza, Dvir Shabtay, Nimrod Talmon, Gerhard Woeginger

Department of Industrial Engineering and Management

Ben-Gurion University of the Negev

Research output: Contribution to journal › Conference article › peer-review

Abstract

We study a scheduling problem where two agents (each equipped with a private set of jobs) compete to perform their respective jobs on a common single machine. Each agent wants to keep the weighted sum of completion times of his jobs below a given (agent-dependent) bound. This problem is known to be NP-hard, even for quite restrictive settings of the problem parameters. We consider parameterized versions of the problem where one of the agents has a small number of jobs (and where this small number constitutes the parameter). The problem becomes much more tangible in this case, and we present three positive algorithmic results for it. Our study is complemented by showing that the general problem is NP-complete even when one agent only has a single job.

Original language	English
Pages (from-to)	55-65
Number of pages	11
Journal	Leibniz International Proceedings in Informatics, LIPIcs
DOIs	https://doi.org/10.4230/LIPIcs.IPEC.2015.55
State	Published - 1 Nov 2015
Event	10th International Symposium on Parameterized and Exact Computation, IPEC 2015 - Patras, Greece Duration: 16 Sep 2015 → 18 Sep 2015

Keywords

Multiagent scheduling
Parameterized complexity

All Science Journal Classification (ASJC) codes

Software

Access to Document

https://doi.org/10.4230/LIPIcs.IPEC.2015.55

Cite this

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title = "Scheduling two competing agents when one agent has significantly fewer jobs",

abstract = "We study a scheduling problem where two agents (each equipped with a private set of jobs) compete to perform their respective jobs on a common single machine. Each agent wants to keep the weighted sum of completion times of his jobs below a given (agent-dependent) bound. This problem is known to be NP-hard, even for quite restrictive settings of the problem parameters. We consider parameterized versions of the problem where one of the agents has a small number of jobs (and where this small number constitutes the parameter). The problem becomes much more tangible in this case, and we present three positive algorithmic results for it. Our study is complemented by showing that the general problem is NP-complete even when one agent only has a single job.",

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note = "10th International Symposium on Parameterized and Exact Computation, IPEC 2015 ; Conference date: 16-09-2015 Through 18-09-2015",

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TY - JOUR

T1 - Scheduling two competing agents when one agent has significantly fewer jobs

AU - Hermelin, Dan

AU - Kubitza, Judith Madeleine

AU - Shabtay, Dvir

AU - Talmon, Nimrod

AU - Woeginger, Gerhard

PY - 2015/11/1

Y1 - 2015/11/1

N2 - We study a scheduling problem where two agents (each equipped with a private set of jobs) compete to perform their respective jobs on a common single machine. Each agent wants to keep the weighted sum of completion times of his jobs below a given (agent-dependent) bound. This problem is known to be NP-hard, even for quite restrictive settings of the problem parameters. We consider parameterized versions of the problem where one of the agents has a small number of jobs (and where this small number constitutes the parameter). The problem becomes much more tangible in this case, and we present three positive algorithmic results for it. Our study is complemented by showing that the general problem is NP-complete even when one agent only has a single job.

AB - We study a scheduling problem where two agents (each equipped with a private set of jobs) compete to perform their respective jobs on a common single machine. Each agent wants to keep the weighted sum of completion times of his jobs below a given (agent-dependent) bound. This problem is known to be NP-hard, even for quite restrictive settings of the problem parameters. We consider parameterized versions of the problem where one of the agents has a small number of jobs (and where this small number constitutes the parameter). The problem becomes much more tangible in this case, and we present three positive algorithmic results for it. Our study is complemented by showing that the general problem is NP-complete even when one agent only has a single job.

KW - Multiagent scheduling

KW - Parameterized complexity

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DO - https://doi.org/10.4230/LIPIcs.IPEC.2015.55

M3 - مقالة من مؤنمر

SN - 1868-8969

SP - 55

EP - 65

JO - Leibniz International Proceedings in Informatics, LIPIcs

JF - Leibniz International Proceedings in Informatics, LIPIcs

T2 - 10th International Symposium on Parameterized and Exact Computation, IPEC 2015

Y2 - 16 September 2015 through 18 September 2015

ER -

Scheduling two competing agents when one agent has significantly fewer jobs

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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