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.
Bibliographical noteFunding Information:
This work was supported in part by the Israel Science Foundation, grant 399/17. The second author was also supported by the United States-Israel Binational Science Foundation, grant 2018095 and the Israel Science Foundation, grant 1074/21.
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
- Dynamic programming
- K-approximation sets and functions
- Strongly polynomial algorithms