Shortest path and distance queries on road networks

Abstract

Computing the shortest path between two given locations in a road network is an important problem that finds applications in various map services and commercial navigation products. The state-of-the-art solutions for the problem can be divided into two categories: spatial-coherence-based methods and vertex-importance-based approaches. The two categories of techniques, however, have not been compared systematically under the same experimental framework, as they were developed from two independent lines of research that do not refer to each other. This renders it difficult for a practitioner to decide which technique should be adopted for a specific application. Furthermore, the experimental evaluation of the existing techniques, as presented in previous work, falls short in several aspects. Some methods were tested only on small road networks with up to one hundred thousand vertices; some approaches were evaluated using distance queries (instead of shortest path queries), namely, queries that ask only for the length of the shortest path; a state-of-the-art technique was examined based on a faulty implementation that led to incorrect query results. To address the above issues, this paper presents a comprehensive comparison of the most advanced spatial-coherence-based and vertex-importance-based approaches. Using a variety of real road networks with up to twenty million vertices, we evaluated each technique in terms of its preprocessing time, space consumption, and query efficiency (for both shortest path and distance queries). Our experimental results reveal the characteristics of different techniques, based on which we provide guidelines on selecting appropriate methods for various scenarios.

Realtime response of shortest path computation

“…Empirical studies exhibit an average response at a scale of fraction of microseconds to shortest path queries. This outperforms Sanders [10] by two orders of magnitude and appears to be the fastest approach referring to the evaluation results [15].…”

“…Over the past two decades, a plethora of techniques have been proposed to address the deficiency of Dijkstra's algorithm by exploiting the characteristics of road networks [15]. These research efforts have produced a number of shortest path algorithms as well as extensive empirical findings regarding the computational performance.…”

Relationship Between Accessibility to Polling Places and Electoral Abstention

“…To obtain the integral accessibility, the travel time vector must be calculated through the "multiple paths" tool of the TRANSCAD software which calculates all the minimum paths between the given nodes, minimizing the chosen variable through the Dijsktra algorithm, in our case travel time (Dijkstra, 1959;Wu et al, 2012). This research seeks to calculate the minimum path of all nodes in the road network (10,312) to the nodes corresponding to the polling places (60), resulting in a travel time matrix of 10 312 x 60 from which the minimum time for each node is extracted, obtaining the vector of minimum travel time paths to the polling places (Cardona, Zuluaga, & Escobar, 2017;Montoya & Escobar, 2017).…”

Alternative routing

“…The goal is to determine whether p is an alternative path to set P , i.e., sufficiently dissimilar to paths pi, pj. In other words, set P is the fixed reference in this test and hence, the similarity of any candidate path depends on its overlap to pi and pj, i.e., the nominator of Equation (2).…”

“…State-of-the-art methods [1,2] compute the shortest path in linear time, even for world-scale road networks. However, determining solely the overall shortest path is not sufficient in many real-world scenarios.…”