Computing at Glasgow University
Paper ID: 9286
DCS Tech Report Number: TR-2010-307

Matching with sizes (or scheduling with processing set restrictions)
Biro,P. McDermid,E.

Publication Type: Tech Report (internal)
Appeared in: DCS Technical Report Series
Page Numbers :
Publisher: Dept of Computing Science, University of Glasgow
Year: 2010

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.

Keywords: couples, Hospitals/Residents problem, scheduling, processing set restrictions, computational complexity, approximation algorithm

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