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### Accelerating Time-Dependent Multi-Criteria Timetable Information is Harder Than Expected

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### Abstract

Speeding up multi-criteria search in real timetable information systems remains a challenge in spite of impressive progress achieved in recent years for related problems in road networks. Our goal is to perform multi-criteria range queries, that is, to find all Pareto-optimal connections with respect to travel time and number of transfers within a given start time interval. This problem can be modeled as a path search problem in a time- and event-dependent graph. In this paper, we investigate two key speed-up techniques for a multi-criteria variant of \textsc{Dijkstra}'s algorithm --- arc flags and contraction --- which seem to be strong candidates for railway networks, too. We describe in detail how these two techniques have to be adapted for a multi-criteria scenario and explain why we can expect only marginal speed-ups (compared to observations in road networks) from a direct implementation. Based on these insights we extend traditional arc-flags to \emph{time-period flags} and introduce \emph{route contraction} as a substitute for node contraction. A computational study on real queries demonstrates that these techniques combined with goal-directed search lead to a speed-up of factor 13.08 over the baseline variant for range queries for a full day.

### BibTeX - Entry

@InProceedings{berger_et_al:OASIcs:2009:2148,
author =	{Annabell Berger and Daniel Delling and Andreas Gebhardt and Matthias M{\"u}ller-Hannemann},
title =	{{Accelerating Time-Dependent Multi-Criteria Timetable Information is Harder Than Expected}},
booktitle =	{9th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'09)},
series =	{OpenAccess Series in Informatics (OASIcs)},
ISBN =	{978-3-939897-11-8},
ISSN =	{2190-6807},
year =	{2009},
volume =	{12},
editor =	{Jens Clausen and Gabriele Di Stefano},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},