Approximation Solutions for Time-Varying Shortest Path Problem

Time-varying network optimization problem, which is NP-complete in the ordinary sense, are traditionally solved by specialized algorithms. This paper considers the time-varying shortest path problem, which can be optimally solved in O T((m+n) ) time, where T is a given integer. For this problem with arbitrary waiting times, we propose an approximate algorithm, which can find an acceptable solution of the problem with O (T (m+n)/k) time complexity such that it evaluates only a subset of the values for t ∈ {0, 1, . . . , T }