Fully Dynamic Maintenance of Arc-Flags in Road Networks

Abstract

Abstract. The problem of finding best routes in road networks can be solved by applying Dijkstra's shortest paths algorithm. Unfortunately, road networks deriving from real-world applications are huge yielding unsustainable times to compute shortest paths. For this reason, great research efforts have been done to accelerate Dijkstra's algorithm on road networks. These efforts have led to the development of a number of speed-up techniques, as for example Arc-Flags, whose aim is to compute additional data in a preprocessing phase in order to accelerate the shortest paths queries in an on-line phase. The main drawback of most of these techniques is that they do not work well in dynamic scenarios. In this paper we propose a new algorithm to update the Arc-Flags of a graph subject to edge weight decrease operations. To check the practical performances of the new algorithm we experimentally analyze it, along with a previously known algorithm for edge weight increase operations, on real-world road networks subject to fully dynamic sequences of operations. Our experiments show a significant speed-up in the updating phase of the Arc-Flags, at the cost of a small space and time overhead in the preprocessing phase.

Fully dynamic update of arc-flags

“…We analyze the theoretical complexity of the new algorithm: on the one hand, we show that it is efficient in terms of the parameters of the input that change as a consequence of a dynamic operation on an edge of the graph; on the other hand, we show that it is not better than the recomputation from scratch of Arc-Flags in the worst case. This extends the results of [10] and [11], where the complexity analysis was not given. -From the experimental point of view, we have completely re-engineered the software used in [10] and [11], and we have adopted more efficient libraries.…”

“…This extends the results of [10] and [11], where the complexity analysis was not given. -From the experimental point of view, we have completely re-engineered the software used in [10] and [11], and we have adopted more efficient libraries. The new implementation represents a big improvement in performance with respect to the results presented in [10] and [11].…”

“…-From the experimental point of view, we have completely re-engineered the software used in [10] and [11], and we have adopted more efficient libraries. The new implementation represents a big improvement in performance with respect to the results presented in [10] and [11]. We performed an experimental study on DynamicRS with the recomputation from scratch of Arc-Flags on road networks subject to fully dynamic sequences of weight increase and weight decrease operations.…”

“…The pseudocode of DecrementalUpdate is given in Figure 2. The procedure uses a binary heap H, which is filled during the first computation of shortest paths (lines [3][4][5][6][7][8][9][10][11][12][13] and it is used during the second computation (lines [14][15][16][17][18][19][20][21][22] to extract the nodes in a greedy order, mimicking Dijkstra's algorithm. The cycle at lines 1-22, considers only boundary nodes b belonging to the Road-Signs of edge (x i , y i ).…”

“…Concerning DynamicRS, we have completely reengineered the C/C++ code used in [10] and [11], and we have adopted more efficient libraries, like Boost Libraries [1]. The new implementation represents a big improvement in the performance of DynamicRS with respect to the results presented in [10] and [11].…”