AUTOMATIC GENERATION OF FPTASes FOR STOCHASTIC MONOTONE DYNAMIC PROGRAMS MADE EASIER

Tzvi Alon; And N.I.R. Halman

doi:10.1137/19m1308633

AUTOMATIC GENERATION OF FPTASes FOR STOCHASTIC MONOTONE DYNAMIC PROGRAMS MADE EASIER

Tzvi Alon, And N.I.R. Halman

Bar-Ilan University - The Alexander Kofkin Faculty of Engineering

Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper we go one step further in the automatic generation of FPTASes for multistage stochastic dynamic programs with scalar state and action spaces, in which the cost-to-go functions have a monotone structure in the state variable. While there exist a few frameworks for automatic generation of FPTASes, so far none of them is general and simple enough to be extensively used. We believe that our framework has these two attributes and has great potential to attract interest from both the operations research and theoretical computer science communities. Moreover, it seems very reasonable that many intractable problems that currently do not admit an FPTAS, can be formulated as DPs that fit into our framework and therefore will admit a first FPTAS. Our results are achieved by a combination of Bellman equation formulations, the technique of K-approximation sets and functions, and in particular the calculus of K-approximation functions.

Original language	English
Pages (from-to)	2679-2722
Number of pages	44
Journal	SIAM Journal on Discrete Mathematics
Volume	35
Issue number	4
DOIs	https://doi.org/10.1137/19m1308633
State	Published - 2021

Bibliographical note

Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics.

Funding

∗Received by the editors December 23, 2019; accepted for publication (in revised form) June 8, 2021; published electronically November 8, 2021. https://doi.org/10.1137/19M1308633 Funding: 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. †Hebrew University of Jerusalem, Israel ([email protected]). ‡Bar Ilan University, Ramat Gan, Israel ([email protected]).

Funders	Funder number
United States-Israel Binational Science Foundation	1074/21, 2018095
Israel Science Foundation	399/17

Keywords

FPTAS
K-approximation sets
dynamic programming
functions

Access to Document

10.1137/19m1308633

Cite this

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AUTOMATIC GENERATION OF FPTASes FOR STOCHASTIC MONOTONE DYNAMIC PROGRAMS MADE EASIER

Abstract

Bibliographical note

Funding

Keywords

Access to Document

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