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The paper we considers the Resource Constrained Shortest Path problem (RCSP). This problem is NPhard 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(|V |) time. The present paper provides a proof of complexity and aproximation of RevTree algorithm.

On Accuracy of Approximation for the Resource Constrained Shortest Path Problem