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
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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A 3/4-Approximation Algorithm for Multiple Subset Sum
Journal of Heuristics
Handbook of Scheduling: Algorithms, Models, and Performance Analysis
Handbook of Scheduling: Algorithms, Models, and Performance Analysis
A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem
SIAM Journal on Computing
The effect of machine availability on the worst-case performance of LPT
Discrete Applied Mathematics
Parameterized Approximation Scheme for the Multiple Knapsack Problem
SIAM Journal on Computing
Decision Support and Optimization in Shutdown and Turnaround Scheduling
INFORMS Journal on Computing
A fast approximation scheme for the multiple knapsack problem
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
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We study two closely related problems in nonpreemptive scheduling of jobs on identical parallel machines. In these two settings there are either fixed jobs or nonavailability intervals during which the machines are not available; in both cases, the objective is to minimize the makespan. Both formulations have different applications, for example, in turnaround scheduling or overlay computing. For both problems we contribute approximation algorithms with an improved ratio of 3/2. For scheduling with fixed jobs, a lower bound of 3/2 on the approximation ratio has been obtained by Scharbrodt et al. [1999]; for scheduling with nonavailability we provide the same lower bound. We use dual approximation, creation of a gap structure, and a PTAS for the multiple subset sum problem, combined with a postprocessing step to assign large jobs.