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.
Highlights
Computing the arrival function from a source node to all other nodes is important for a lot of transportation applications
time-dependent shortest path problem (TDSP) can be defined as minimizing the travel time over the set Ps,d of all paths in G from the source node s to the destination node d: fd = min{ fp(t)|p ∈ Ps,d}, (1)
The main task is to develop an algorithm which solves TDSP with the given maximum relative error and is effective for a real road network. It follows that we focused on the ε-approximation of the label correcting modification of Dijkstra’s algorithm (LCA)
Summary
Computing the arrival function from a source node to all other nodes is important for a lot of transportation applications. Given a directed graph G = (V, E), a source node s ∈ V, we want to know the travel time between the source node s and all other nodes for every departure time (in some literature called a travel time profile). The problem with an increase in the number of linear pieces can be solved using the ε-approximation of the resulting arrival function This approach reduces the number of linear pieces, and reduces memory requirements as well as computation time. The main idea is to perform a simplification of the arrival functions during the computation with a suitable maximum absolute error so that the relative error ε is maintained. The idea is that the original departure time interval is split into subintervals, and the number of edge relaxations is reduced These subintervals are independent too, so the parallelization or distribution of computation is possible and effective
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