On Accuracy of Approximation for the Resource Constrained Shortest Path Problem - Soldatenko, Aleksandr A. (Journal of Siberian Federal University. Mathematics & Physics, 2019)
The paper we considers the Resource Constrained Shortest Path problem (RCSP). This problem is NP- hard extension of a well-known shortest path problem in the directed graph G = (V;E). In the RCSP problem each arc e from E has a cost w(e) and additional weight functions ri(e); i = 1; : : : ; k, which specifying its requirements from a finite set of resource. A polynomial time ϵ-approximation algorithm RevTree based on node labeling method is presented in the paper. The main advantage of the RevTree algorithm over existing ones is its ability to produce ϵ approximation of the RCSP problem in O(jV j2) time. The present paper provides a proof of complexity and aproximation of RevTree algorithm