Time-Dependent SHARC-Routing

Abstract

In recent years, many speed-up techniques for Dijkstra's algorithm have been developed that make the computation of shortest paths in static road networks a matter of microseconds. However, only few of those techniques work in timedependent networks which, unfortunately, appear quite frequently in reality: Roads are predictably congested by traffic jams, and efficient timetable information systems rely on time-dependent networks. Hence, a fast technique for routing in such networks is needed.In this work, we present an efficient time-dependent route planning algorithm. It is based on our recently introduced SHARC algorithm, which we adapt by augmenting its basic ingredients such that correctness can still be guaranteed in a time-dependent scenario. As a result, we are able to efficiently compute exact shortest paths in timedependent continental-sized transportation networks, both of roads and of railways. It should be noted that time-dependent SHARC was the first efficient algorithm for time-dependent route planning.Keywords Algorithm engineering · Graph algorithms · Time-dependent shortest paths · Timetable information IntroductionComputing shortest paths in graphs is used in many real-world applications like route planning in road networks, timetable information for railways, or scheduling for airplanes. In general, DIJKSTRA's algorithm [12] finds a shortest path between a given Partially supported by the Future and Emerging Technologies Unit of EC (IST priority-6th FP), under contract no. FP6-021235-2 (project ARRIVAL) and the DFG (project WA 654/16-1).

Batch Dynamic Single-Source Shortest-Path Algorithms: An Experimental Study

“…We always apply a binary heap when a priority queue is needed. We use the graph datastructure that is also applied in [20][21][22]. There, the datastructure has experimentally shown to perform well in the context of shortest-path computation on sparse graphs.…”

Core Routing on Dynamic Time-Dependent Road Networks

“…For the contraction phase, i.e., the routine that selects which nodes have to be bypassed and then adds shortcuts to preserve distances between remaining nodes, we use the algorithm proposed in [8]. We define the expansion [19] of a node u as the quotient between the number of added shortcuts and the number of edges removed if u is bypassed, and the hop-number of a shortcut as the number of edges that the shortcut represents.…”

“…Note that the contraction of u may influence the bypassability score of adjacent nodes, so these scores must be recomputed after a node is chosen. As suggested by [8], we give a larger importance to the expansion of a node when determining its bypassability score, thus using a coefficient of 10 for this factor in the linear combination, whereas the other two factors are added with unitary coefficient. This heuristic is motivated by the good results obtained in [8]; experiments in [16] show that all "reasonable" heuristics to determine the bypassability score perform well in practice.…”

“…This step can be performed by computing the cost function d * (u, v) on the graph (V C , A C \ {(u, v)}) with a label-correcting algorithm (Section 1.3) and comparing d * (u, v) with c(u, v). If d * (u, v)(τ ) < c(u, v, τ ) ∀τ ∈ T , then the arc (u, v) is not necessary, as there is a shorter path between u and v for all possible departure times (see also [8]). Whenever a shortcut between two nodes u, v ∈ V is added, its cost for each time instant of the time interval is computed running a label-correcting algorithm between u and v (Section 1.3).…”

“…For comparison, we also report the results on the same road network for the time-dependent versions of Dijkstra, unidirectional ALT, TDALT and the SHARC algorithm. SHARC, introduced in [2] and augmented to time-dependent scenarios in [8], is a unidirectional technique based on arc-flags [26] and shortcuts (for details, see [2,8]). In particular, Dijkstra's algorithm is used as a baseline to measure speedup factors, while SHARC is the fastest known algorithm for time-dependent shortest paths, although it is not able to deal with dynamic scenarios.…”