Space-Efficient, Fast and Exact Routing in Time-Dependent Road Networks

Abstract

We study the problem of quickly computing point-to-point shortest paths in massive road networks with traffic predictions. Incorporating traffic predictions into routing allows, for example, to avoid commuter traffic congestions. Existing techniques follow a two-phase approach: In a preprocessing step, an index is built. The index depends on the road network and the traffic patterns but not on the path start and end. The latter are the input of the query phase, in which shortest paths are computed. All existing techniques have large index size, slow query running times or may compute suboptimal paths. In this work, we introduce CATCHUp (Customizable Approximated Time-dependent Contraction Hierarchies through Unpacking), the first algorithm that simultaneously achieves all three objectives. The core idea of CATCHUp is to store paths instead of travel times at shortcuts. Shortcut travel times are derived lazily from the stored paths. We perform an experimental study on a set of real world instances and compare our approach with state-of-the-art techniques. Our approach achieves the fastest preprocessing, competitive query running times and up to 38 times smaller indexes than competing approaches.

Improving Time-Dependent Contraction Hierarchies

“…The implementation is also known as KaTCH. In a recent study (Strasser, Wagner, and Zeitz 2021), it was shown that KaTCH is the state-of-theart algorithm and outperforms a range of optimal algorithms, including CATCHUp (Strasser, Wagner, and Zeitz 2021), TD-CALT (Delling and Nannicini 2012), and TD-SHARC (Delling 2011). Meanwhile, our approaches: (i) the Single-layer TCH (STCH) is built by splitting the time domain into 24 hourly buckets and the upper-bound t u is set to 4 hours as no trip in our tested maps exceeds this limit.…”

“…Finally, BTCH unpacks the tch-path using the middle node profile maintained on the corresponding shortcut edges, and the optimal path sp(s, d, t) is returned. BTCH remains state-of-the-art for time-dependent routing (Strasser, Wagner, and Zeitz 2021).…”

Vehicle Routing with Time-Dependent Travel Times: Theory, Practice, and Benchmarks

“…Batz, Geisberger, Sanders, and Vetter [9] showed how to preprocess a road network with time-dependent travel times in order to allow relatively fast shortest path queries. A less memory-consuming variant was proposed by [43]. While a contraction hierarchy needs to be recomputed only when the road network changes, [21] proposed an additional instance-specific preprocessing to speed up fastest-path queries.…”

NP-hardness of shortest path problems in networks with non-FIFO time-dependent travel times

“…As an extensive overview is beyond the scope of this work, we refer to the survey in [2]. Most practical works assume that all travel times adhere to the FIFO property or that arbitrary waiting is allowed [3][4][5][6]. An exception is [7] where routing for truck drivers considering temporary driving bans is studied.…”

“…However, the paper just states that the hardness can be shown (second paragraph of Section 3.2) but does not provide any evidence. Some works [7,6,3] state the hardness referring to an unpublished manuscript by Orda and Rom [11]. We were not able to find this manuscript in any public source but could only obtain it through personal contact with authors.…”