We define a collection of new problems referred to as ``machine activation'' problems. The central framework we introduce considers a collection of M machines (unrelated or related), with machine $i$ having an activation cost of $a_i$. There is also a collection of N jobs that need to be performed, and $p_{ij}$ is the processing time of job $j$ on machine $i$. Standard scheduling models assume that the set of machines is fixed and all machines are available. We assume that there is an activation cost budget of $A$ -- we would like to select a subset S of the machines to activate with total cost $a(S)le A$ and find a schedule for the jobs on the machines in $S$ minimizing the makespan. In this work we develop bi-criteria approximation algorithms for this problem based on both LP rounding and a greedy approach.
@InProceedings{khuller_et_al:DagSemProc.10071.5, author = {Khuller, Samir and Li, Jian and Saha, Barna}, title = {{Energy Efficient Scheduling via Partial Shutdown}}, booktitle = {Scheduling}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2010}, volume = {10071}, editor = {Susanne Albers and Sanjoy K. Baruah and Rolf H. M\"{o}hring and Kirk Pruhs}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10071.5}, URN = {urn:nbn:de:0030-drops-25435}, doi = {10.4230/DagSemProc.10071.5}, annote = {Keywords: Unrelated parallel machine scheduling, approximation algorithms} }
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