Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
On the exact upper bound for the MULTIFIT processor scheduling algorithm
Annals of Operations Research
Parallel machines scheduling with nonsimultaneous machine available time
Discrete Applied Mathematics
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
The worst-case analysis of the MULTIFIT algorithm for scheduling nonsimultaneous parallel machines
Discrete Applied Mathematics
A note on “parallel machine scheduling with non-simultaneous machine available time”
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Wire routing by optimizing channel assignment within large apertures
DAC '71 Proceedings of the 8th Design Automation Workshop
Computers and Operations Research
Improved approximation algorithms for scheduling with fixed jobs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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We consider the makespan minimization parallel machine scheduling problem where each machine may be unavailable for a known time interval. For this problem, we investigate how the worst-case behavior of the longest processing time first algorithm (LPT) is affected by the availability of machines. In particular, for given m machines, we analyze the cases where arbitrary number, λ, ranging from one to m - 1, machines are unavailable simultaneously. Then, we show that the makespan of the schedule generated by LPT is never more than the tight worst-case bound of 1 + ½ ⌊m/(m - λ)⌋ times the optimum makespan.