Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Parallel machines scheduling with nonsimultaneous machine available time
Discrete Applied Mathematics
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Approximability of scheduling with fixed jobs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
A PTAS for the multiple knapsack problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A PTAS for the Multiple Subset Sum Problem with different knapsack capacities
Information Processing Letters
A note on “parallel machine scheduling with non-simultaneous machine available time”
Discrete Applied Mathematics
A Near-Optimal Solution to a Two-Dimensional Cutting Stock Problem
Mathematics of Operations Research
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
The effect of machine availability on the worst-case performance of LPT
Discrete Applied Mathematics
A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem
SIAM Journal on Computing
Parameterized approximation scheme for the multiple knapsack problem
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Approximation algorithms for scheduling with reservations
HiPC'07 Proceedings of the 14th international conference on High performance computing
A Survey on Approximation Algorithms for Scheduling with Machine Unavailability
Algorithmics of Large and Complex Networks
Approximation schemes for scheduling with availability constraints
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Approximation schemes for parallel machine scheduling with availability constraints
Discrete Applied Mathematics
Approximation algorithms for scheduling and packing problems
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Faster approximation algorithms for scheduling with fixed jobs
CATS '11 Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119
Faster approximation algorithms for scheduling with fixed jobs
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
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We study two closely related problems in non-preemptive scheduling of sequential jobs on identical parallel machines. In these two settings there are either fixed jobs or non-availability intervals during which the machines are not available; in either case, the objective is to minimize the makespan. Both formulations have different applications, e.g. in turnaround scheduling or overlay computing. For both problems we contribute approximation algorithms with an improved ratio of 3/2 + ε, respectively. For scheduling with fixed jobs, a lower bound of 3/2 on the approximation ratio has been obtained by Scharbrodt, Steger & Weisser; for scheduling with non-availability we provide the same lower bound. In total, our approximation ratio for both problems is essentially tight via suitable inapproximability results. We use dual approximation, creation of a gap structure and job configurations, and a PTAS for the multiple subset sum problem. However, the main feature of our algorithms is a new technique for the assignment of large jobs via flexible rounding. Our new technique is based on an interesting cyclic shifting argument in combination with a network flow model for the assignment of jobs to large gaps.