Fast Exact Computation of Isochrones in Road Networks

Abstract

We study the problem of computing isochrones in road networks, where the objective is to identify the region that is reachable from a given source within a certain amount of time. While there is a wide range of practical applications for this problem (e. g., reachability analyses, geomarketing, visualizing the cruising range of a vehicle), there has been little research on fast computation of isochrones on large, realistic inputs. In this work, we formalize the notion of isochrones in road networks and present a basic approach for the resulting problem based on Dijkstra's algorithm. Moreover, we consider several speedup techniques that are based on previous approaches for one-tomany shortest path computation (or similar scenarios). In contrast to such related problems, the set of targets is not part of the input when computing isochrones. We extend known Multilevel Dijkstra techniques (such as CRP) to the isochrone scenario, adapting a previous technique called isoGRASP to our problem setting (thereby, enabling faster queries). Moreover, we introduce a family of algorithms based on (single-level) graph partitions, following different strategies to exploit the efficient access patterns of PHAST, a well-known approach towards one-to-all queries. Our experimental study reveals that all speedup techniques allow fast isochrone computation on input graphs at continental scale, while providing different tradeoffs between preprocessing effort, space consumption, and query performance. Finally, we demonstrate that all techniques scale well when run in parallel, decreasing query times to a few milliseconds (orders of magnitude faster than the basic approach) and enabling even interactive applications. on practical algorithms for routing in road networks [2]. Most work focused on computing distances (or shortest paths) between pairs (or sets) of vertices. On the other hand, isochrones (more generally, isolines) are defined as curves of constant distance (from a given source). Thereby, isochrones represent the area that is in range for a given time limit (or some other limited resource). Hence, rather than actual distances, information about the subgraph within range is required. Isolines are relevant in a wide range of applications, such as reachability analyses [3,17,18], geomarketing [13], range visualization for (electric) vehicles [20], and a variety of online applications [22].Related Work. Dijkstra's well-known algorithm [12] computes shortest paths from a given source to all (reachable) vertices in (almost) linear time. The MINE algorithm [17] is a Dijkstra-based search to compute isochrones in transportation networks, using a spatial network database. An improved variant, MIMEX [18], has reduced space requirements. Both approaches work on databases, prohibiting interactive applications (with running times beyond the order of minutes).Regarding shortest-path computation, on the other hand, various speedup techniques [2] were developed for faster queries, using an offline preprocessing phase (sometimes including an ad...

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Scalable Isocontour Visualization in Road Networks via Minimum-Link Paths

“…Speedup techniques [1] are a common approach for much faster queries in practice. A recent work [3] presents techniques extending the basic approach described above that enable fast computation of boundary edges (considering the special case of len ≡ cons). Since they can be adapted to our scenario, we focus on the remaining steps for computing range polygons.…”

“…Consequently, such approaches did not provide significant speedup in preliminary experiments. Moreover, determining the reachable subgraph of G p in a separate step simplifies the integration of speedup techniques for the more expensive search algorithm [3].…”

“…ing phase and an online query phase. Recently, some speedup techniques were extended to the isochrone scenario [3,12], enabling query times in the order of milliseconds. Yet, these approaches only deal with the computation of the reachable subgraph, rather than visualization of isocontours.…”