Approximation of Pareto optima in multiple-objective, shortest-path problems
Operations Research
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Annals of Operations Research
Approximation schemes for the restricted shortest path problem
Mathematics of Operations Research
Computing Partitions with Applications to the Knapsack Problem
Journal of the ACM (JACM)
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Algorithms for Scheduling Independent Tasks
Journal of the ACM (JACM)
Exact and Approximate Algorithms for Scheduling Nonidentical Processors
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
An improved FPTAS for restricted shortest path
Information Processing Letters
A simple efficient approximation scheme for the restricted shortest path problem
Operations Research Letters
Clustered subset selection and its applications on it service metrics
Proceedings of the 17th ACM conference on Information and knowledge management
Constraint-based local search for fields partitioning problem
Proceedings of the Second Symposium on Information and Communication Technology
Universal sequencing on a single machine
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Algorithms and complexity for periodic real-time scheduling
ACM Transactions on Algorithms (TALG)
A complexity and approximability study of the bilevel knapsack problem
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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In this paper we develop an easily applicable algorithmic technique/tool for developing approximation schemes for certain types of combinatorial optimization problems. Special cases that are covered by our result show up in many places in the literature. For every such special case, a particular rounding trick has been implemented in a slightly different way, with slightly different arguments, and with slightly different worst case estimations. Usually, the rounding procedure depended on certain upper or lower bounds on the optimal objective value that have to be justified in a separate argument. Our easily applied result unifies many of these results, and sometimes it even leads to a simpler proof. We demonstrate how our result can be easily applied to a broad family of combinatorial optimization problems. As a special case, we derive the existence of an FPTAS for the scheduling problem of minimizing the weighted number of late jobs under release dates and preemption on a single machine. The approximability status of this problem has been open for some time.