Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
NP-complete stable matching problems
Journal of Algorithms
Approximation schemes for scheduling
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
A Polynomial Algorithm for Multiprocessor Scheduling with Two Job Lengths
Mathematics of Operations Research
ACM Transactions on Algorithms (TALG)
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Scheduling unit length jobs with parallel nested machine processing set restrictions
Computers and Operations Research
Semi-matchings for bipartite graphs and load balancing
Journal of Algorithms
Algorithmica - Special Issue: Matching Under Preferences; Guest Editors: David F. Manlove, Robert W. Irving and Kazuo Iwama
Parallel machine scheduling with nested job assignment restrictions
Operations Research Letters
Stable assignment with couples: Parameterized complexity and local search
Discrete Optimization
An optimal rounding gives a better approximation for scheduling unrelated machines
Operations Research Letters
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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 2^k-1 for the case where each job has a size taken from the set {1,2,4,...,2^k} (for any constant integer k). We show that the above two problems become polynomial-time solvable if the processing sets are nested.