The ε-Approximation of the Time-Dependent Shortest Path Problem Solution for All Departure Times

Abstract

In this paper, the shortest paths search for all departure times (profile search) are discussed. This problem is called a time-dependent shortest path problem (TDSP) and is suitable for time-dependent travel-time analysis. Particularly, this paper deals with the ε -approximation of profile search computation. The proposed algorithms are based on a label correcting modification of Dijkstra’s algorithm (LCA). The main idea of the algorithm is to simplify the arrival function after every relaxation step so that the maximum relative error is maintained. When the maximum relative error is 0.001, the proposed solution saves more than 97% of breakpoints and 80% of time compared to the exact version of LCA. Furthermore, the runtime can be improved by other 15% to 40% using heuristic splitting of the original departure time interval to several subintervals. The algorithms we developed can be used as a precomputation step in other routing algorithms or for some travel time analysis.

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