On the minimum risk-sum path problem

Authors:
Xujin Chen;Jie Hu;Xiaodong Hu
Affiliations:
Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, China;Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, China;Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, China
Venue:
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
Year:
2007

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Abstract

This paper presents efficient algorithms for the minimum risk-sum path problem which arises in a variety of applications. Given a source-destination node pair in a network G = (V, E), where each link e in G can be traveled using time xe in a prespecified interval [le, ue] while taking risk ue-xe/ue-le, the minimum risk-sum path problem is to find a path in G from source to destination, together with an assignment of travel times along each link on the path, so that the total travel time of the path is no more than a given constant and the risk sum over the links on the path is minimized. In this paper, we solve the minimum risk-sum path problem optimally in O(|V|3|E|) time.