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Open AccessArticle

Journey Planning Algorithms for Massive Delay-Prone Transit Networks

by Mattia D'Emidio 1,†, Imran Khan 2,*,† and Daniele Frigioni 1
Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, Via Vetoio, 67100 L’Aquila, Italy
Gran Sasso Science Institute (GSSI), Viale Francesco Crispi, 67100 L’Aquila, Italy
Author to whom correspondence should be addressed.
Parts of this paper appeared in extended abstract form within the proceedings of the 19th International Conference on Computational Science and its Applications (ICCSA2019), Saint Petersburg, Russia, 1–4 July 2019.
Algorithms 2020, 13(1), 2;
Received: 29 September 2019 / Revised: 4 December 2019 / Accepted: 10 December 2019 / Published: 18 December 2019
This paper studies the journey planning problem in the context of transit networks. Given
the timetable of a schedule-based transportation system (consisting, e.g., of trains, buses, etc.),
the problem seeks journeys optimizing some criteria. Specifically, it seeks to answer natural queries
such as, for example, “find a journey starting from a source stop and arriving at a target stop as early
as possible”. The fastest approach for answering to these queries, yielding the smallest average query
time even on very large networks, is the Public Transit Labeling framework, proposed for the first
time in Delling et al., SEA 2015. This method combines three main ingredients: (i) a graph-based
representation of the schedule of the transit network; (ii) a labeling of such graph encoding its
transitive closure (computed via a time-consuming pre-processing); (iii) an efficient query algorithm
exploiting both (i) and (ii) to answer quickly to queries of interest at runtime. Unfortunately, while
transit networks’ timetables are inherently dynamic (they are often subject to delays or disruptions),
PTL is not natively designed to handle updates in the schedule—even after a single change,
precomputed data may become outdated and queries can return incorrect results. This is a major
limitation, especially when dealing with massively sized inputs (e.g., metropolitan or continental
sized networks), as recomputing the labeling from scratch, after each change, yields unsustainable
time overheads that are not compatible with interactive applications. In this work, we introduce a new
framework that extends PTL to function in delay-prone transit networks. In particular, we provide
a new set of algorithms able to update both the graph and the precomputed labeling whenever
a delay affects the network, without performing any recomputation from scratch. We demonstrate
the effectiveness of our solution through an extensive experimental evaluation conducted on
real-world networks. Our experiments show that: (i) the update time required by the new algorithms
is, on average, orders of magnitude smaller than that required by the recomputation from scratch via
PTL; (ii) the updated graph and labeling induce both query time performance and space overhead that
are equivalent to those that are obtained by the recomputation from scratch via PTL. This suggests that
our new solution is an effective approach to handling the journey planning problem in delay-prone
transit networks.
Keywords: journey planning; transit networks; dynamic graph algorithms; algorithms engineering; massive datasets; experimental algorithmics journey planning; transit networks; dynamic graph algorithms; algorithms engineering; massive datasets; experimental algorithmics
MDPI and ACS Style

D'Emidio, M.; Khan, I.; Frigioni, D. Journey Planning Algorithms for Massive Delay-Prone Transit Networks. Algorithms 2020, 13, 2.

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