Matching with sizes (or scheduling with processing set restrictions)

Biró, P. and McDermid, E. (2010) Matching with sizes (or scheduling with processing set restrictions). Electronic Notes in Discrete Mathematics, 36(1), pp. 335-342. (doi:10.1016/j.endm.2010.05.043)

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Abstract

Matching problems on bipartite graphs where the entities on one side may have different sizes are intimately related to scheduling problems with processing set restrictions. We survey the close relationship between these two problems, and give new approximation algorithms for the (NP-hard) variations of the problems in which the sizes of the jobs are restricted. Specifically, we give an approximation algorithm with an additive error of one when the sizes of the jobs are either 1 or 2, and generalise this to an approximation algorithm with an additive error of k2−12k−1 for the case where each job has a size taken from the set {1,2,4,…,k2}{1,2,4,…,2k} (for any constant integer k). We show that the above two problems become polynomial time solvable if the processing sets are nested.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:McDermid, Mr Eric
Authors: Biró, P., and McDermid, E.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Electronic Notes in Discrete Mathematics
Publisher:Elsevier
ISSN:15710653

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
436361MATCH-UP - matching under preferences - algorithms and complexityRobert IrvingEngineering & Physical Sciences Research Council (EPSRC)EP/E011993/1COM - COMPUTING SCIENCE