When Does a Dynamic Programming Formulation Guarantee the Existence of a Fully Polynomial Time Approximation Scheme (FPTAS)?

We derive results of the following flavor: If a combinatorial optimization problem can be formulated via a dynamic program of a certain structure and if the involved cost and transition functions satisfy certain arithmetical and structural conditions, then the optimization problem automatically poss...

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Bibliographic Details
Published in:INFORMS journal on computing 2000-12, Vol.12 (1), p.57-74
Main Author: Woeginger, Gerhard J
Format: Article
Language:English
Subjects:
Algorithms
approximate algorithm
Approximation
Dynamic programming
FPTAS
Optimization
Scheduling
Studies
worst-case analysis
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Summary:We derive results of the following flavor: If a combinatorial optimization problem can be formulated via a dynamic program of a certain structure and if the involved cost and transition functions satisfy certain arithmetical and structural conditions, then the optimization problem automatically possesses a fully polynomial time approximation scheme (FPTAS). Our characterizations provide a natural and uniform approach to fully polynomial time approximation schemes. We illustrate their strength and generality by deducing from them the existence of FPTASs for a multitude of scheduling problems. Many known approximability results follow as corollaries from our main result.
ISSN:1091-9856
1526-5528
1091-9856
DOI:10.1287/ijoc.12.1.57.11901