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

Authors:
Gerhard J. Woeginger
Affiliations:
-
Venue:
INFORMS Journal on Computing
Year:
2000

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Abstract

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.