A fully polynomial time approximation scheme for the probability maximizing shortest path problem

Jisun Lee, Seulgi Joung and Kyungsik Lee

European Journal of Operational Research, 2022, vol. 300, issue 1, 35-45

Abstract: In this paper, we consider a probability maximizing shortest path problem. For a given directed graph with the length of each arc being an independent normal random variable with rational mean and standard deviation, the problem is to find a simple s−t path that maximizes the probability of arriving at the destination within a given limit. We first prove that the problem is NP-hard even on directed acyclic graphs with the mean of the length of each arc being restricted to an integer. Then, we present pseudo-polynomial time exact algorithms for the problem along with nontrivial special cases that can be solved in polynomial time. Finally, we present a fully polynomial time approximation scheme (FPTAS) that iteratively solves deterministic shortest path problems. The structure of the proposed approximation scheme can be applied to devise FPTAS for other probability maximizing combinatorial optimization problems once the corresponding deterministic problems are polynomially solvable.

Keywords: Combinatorial optimization; Shortest path; Probability maximization; Exact algorithm; Fully polynomial time approximation scheme (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:300:y:2022:i:1:p:35-45

DOI: 10.1016/j.ejor.2021.10.018

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