Scheduling two competing agents when one agent has significantly fewer jobs. (English) Zbl 1378.68021
Husfeldt, Thore (ed.) et al., 10th international symposium on parameterized and exact computation, IPEC 2015, Patras, Greece, September 16–18, 2015. Proceedings. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik (ISBN 978-3-939897-92-7). LIPIcs – Leibniz International Proceedings in Informatics 43, 55-65 (2015).
Summary: 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.
For the entire collection see [Zbl 1338.68007].
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.
For the entire collection see [Zbl 1338.68007].
MSC:
| 68M20 | Performance evaluation, queueing, and scheduling in the context of computer systems |
| 68Q17 | Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) |
| 68Q25 | Analysis of algorithms and problem complexity |
