Approximation schemes for a class of subset selection problems

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 rou...

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Veröffentlicht in:Theoretical computer science Jg. 382; H. 2; S. 151 - 156
Hauptverfasser: Pruhs, Kirk, Woeginger, Gerhard J.
Format: Journal Article Tagungsbericht
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 31.08.2007
Elsevier
Schlagworte:
Applied sciences
Approximation algorithm
Approximation scheme
Calculus of variations and optimal control
Combinatorial optimization
Computer science; control theory; systems
Computer systems performance. Reliability
Exact sciences and technology
FPTAS
Mathematical analysis
Mathematics
Miscellaneous
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Pseudo-polynomial algorithm
Scheduling theory
Sciences and techniques of general use
Software
Theoretical computing
Worst case analysis
Pseudo-polynomial algorithm
Approximation scheme
Approximation algorithm
FPTAS
Combinatorial optimization
Scheduling theory
Worst case analysis
Polynomial
Lower bound
Approximation
Computer theory
Combinatorial problem
Estimation
Optimization method
Algorithmics
Scheduling
Implementation
Selection problem
Upper bound
Proof
Procedure
Single machine
ISSN:0304-3975, 1879-2294
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Beschreibung
Zusammenfassung: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.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2007.03.006