We study non-preemptive scheduling problems on identical parallel machines and uniformly related machines under both resource constraints and general precedence constraints between jobs. Our first result is an O(logn)-approximation algorithm for the objective of minimizing the makespan on parallel identical machines under resource and general precedence constraints. We then use this result as a subroutine to obtain an O(logn)-approximation algorithm for the more general objective of minimizing the total weighted completion time on parallel identical machines under both constraints. Finally, we present an O(logm logn)-approximation algorithm for scheduling under these constraints on uniformly related machines. We show that these results can all be generalized to include the case where each job has a release time. This is the first upper bound on the approximability of this class of scheduling problems where both resource and general precedence constraints must be satisfied simultaneously.
@InProceedings{demirci_et_al:LIPIcs.STACS.2018.25, author = {Demirci, G\"{o}kalp and Hoffmann, Henry and Kim, David H. K.}, title = {{Approximation Algorithms for Scheduling with Resource and Precedence Constraints}}, booktitle = {35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)}, pages = {25:1--25:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-062-0}, ISSN = {1868-8969}, year = {2018}, volume = {96}, editor = {Niedermeier, Rolf and Vall\'{e}e, Brigitte}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.25}, URN = {urn:nbn:de:0030-drops-85319}, doi = {10.4230/LIPIcs.STACS.2018.25}, annote = {Keywords: scheduling, resource, precedence, weighted completion time} }
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