We consider the problem of quickly computing shortest paths in weighted graphs. Often, this is achieved in two phases: 1) derive auxiliary data in an expensive preprocessing phase, 2) use this auxiliary data to speedup the query phase. By adding a fast weight-customization phase, we extend Contraction Hierarchies to support a three-phase workflow: The expensive preprocessing is split into a phase exploiting solely the unweighted topology of the graph, as well as a lightweight phase that adapts the auxiliary data to a specific weight. We achieve this by basing our Customizable Contraction Hierarchies on nested dissection orders. We provide an in-depth experimental analysis on large road and game maps that shows that Customizable Contraction Hierarchies are a very practicable solution in scenarios where edge weights often change.

This paper studies the problem of computing optimal journeys in dynamic public transit networks. We introduce a novel algorithmic framework, called Connection Scan Algorithm (CSA), to compute journeys. It organizes data as a single array of connections, which it scans once per query. Despite its simplicity, our algorithm is very versatile. We use it to solve earliest arrival and multi-criteria profile queries. Moreover, we extend it to handle the minimum expected arrival time (MEAT) problem, which incorporates stochastic delays on the vehicles and asks for a set of (alternative) journeys that in its entirety minimizes the user's expected arrival time at the destination. Our experiments on the dense metropolitan network of London show that CSA computes MEAT queries, our most complex scenario, in 272 ms on average.

We introduce the Connection Scan Algorithm (CSA) to efficiently answer queries to timetable information systems. The input consists, in the simplest setting, of a source position and a desired target position. The output consist is a sequence of vehicles such as trains or buses that a traveler should take to get from the source to the target. We study several problem variations such as the earliest arrival and profile problems. We present algorithm variants that only optimize the arrival time or additionally optimize the number of transfers in the Pareto sense. An advantage of CSA is that is can easily adjust to changes in the timetable, allowing the easy incorporation of known vehicle delays. We additionally introduce the Minimum Expected Arrival Time (MEAT) problem to handle possible, uncertain, future vehicle delays. We present a solution to the MEAT problem that is based upon CSA. Finally, we extend CSA using the multilevel overlay paradigm to answer complex queries on nation-wide integrated timetables with trains and buses.

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We study the journey planning problem in public transit networks. Developing efficient preprocessing-based speedup techniques for this problem has been challenging: current approaches either require massive preprocessing effort or provide limited speedups. Leveraging recent advances in Hub Labeling, the fastest algorithm for road networks, we revisit the well-known time-expanded model for public transit. Exploiting domainspecific properties, we provide simple and efficient algorithms for the earliest arrival, profile, and multicriteria problems, with queries that are orders of magnitude faster than the state of the art.