Strongly Polynomial FPTASes for Monotone Dynamic Programs

In this paper we introduce a framework for the automatic generation of Strongly Polynomial Fully Polynomial Time Approximation Schemes (SFPTASes) for monotone dynamic programs. While some ad-hoc SFPTASes for specific problems are already known, this is the first framework yielding such SFPTASes. In...

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Bibliographic Details
Published in:Algorithmica Vol. 84; no. 10; pp. 2785 - 2819
Main Authors: Alon, Tzvi, Halman, Nir
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2022
Springer Nature B.V
Subjects:
Agents (artificial intelligence)
Algorithm Analysis and Problem Complexity
Algorithms
Approximation
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Mathematical analysis
Mathematics of Computing
Polynomials
Theory of Computation
Strongly polynomial algorithms
approximation sets and functions
Dynamic programming
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary:In this paper we introduce a framework for the automatic generation of Strongly Polynomial Fully Polynomial Time Approximation Schemes (SFPTASes) for monotone dynamic programs. While some ad-hoc SFPTASes for specific problems are already known, this is the first framework yielding such SFPTASes. In addition, it is possible to use our algorithm to get efficient (non strongly polynomial) FPTASes. Our results are derived by improving former (non strongly polynomial) FPTASes which were designed via the method of K -approximation sets and functions. We demonstrate our SFPTAS framework on five application problems, namely, 0/1 Knapsack, counting 0/1 Knapsack, Counting s - t paths, Mobile agent routing and Counting n -tuples, for the last problem we get the fastest SFPTAS known to date. In addition, we use our algorithm to get the fastest (non strongly polynomial) FPTASes for the following other three application problems: Stochastic ordered knapsack, Bi-criteria path problem with maximum survival probability and Minimizing the makespan of deteriorating jobs.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-022-00954-8