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Scheduling Two Competing Agents When One Agent Has Significantly Fewer Jobs

Authors Danny Hermelin, Judith-Madeleine Kubitza, Dvir Shabtay, Nimrod Talmon, Gerhard Woeginger

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Danny Hermelin
Judith-Madeleine Kubitza
Dvir Shabtay
Nimrod Talmon
Gerhard Woeginger

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Danny Hermelin, Judith-Madeleine Kubitza, Dvir Shabtay, Nimrod Talmon, and Gerhard Woeginger. Scheduling Two Competing Agents When One Agent Has Significantly Fewer Jobs. In 10th International Symposium on Parameterized and Exact Computation (IPEC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 43, pp. 55-65, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.IPEC.2015.55

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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Keywords
  • Parameterized Complexity
  • Multiagent Scheduling

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