Matching with sizes (or scheduling with processing set restrictions)

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) variation...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 164; pp. 61 - 67
Main Authors: Biró, Péter, McDermid, Eric
Format: Journal Article
Language:English
Published: Elsevier B.V 19.02.2014
Subjects:
Additives
Algorithms
Approximation
Approximation algorithms
Computational complexity
Constrictions
Couples
Errors
Hospitals/Residents problem
Matching
Mathematical analysis
Processing set restrictions
Scheduling
Approximation algorithms
Hospitals/Residents problem
Scheduling
Couples
Computational complexity
Processing set restrictions
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary: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 2k−1 for the case where each job has a size taken from the set {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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2011.11.003