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 FlowCutter, a novel algorithm to compute a set of edge cuts or node separators that optimize cut size and balance in the Pareto-sense. Our core algorithm heuristically solves the balanced connected st-edge-cut problem, where two given nodes s and t must be separated by removing edges to obtain two connected parts. Using the core algorithm as subroutine, we build variants that compute node separators which are independent of s and t. From the computed Pareto-set, we can identify cuts with a particularly good tradeoff between cut size and balance that can be used to compute contraction and minimum fill-in orders, which can be used in Customizable Contraction Hierarchies (CCH), a speed-up technique for shortest path computations. Our core algorithm runs in O(c|E|) time where E is the set of edges and c is the size of the largest outputted cut. This makes it wellsuited for separating large graphs with small cuts, such as road graphs, which is the primary application motivating our research. For road graphs, we present an extensive experimental study demonstrating that FlowCutter outperforms the current state-of-the-art both in terms of cut sizes and CCH performance. By evaluating FlowCutter on a standard graph partitioning benchmark, we further show that FlowCutter also finds small, balanced cuts on non-road graphs. Another application is the computation of small tree-decompositions.To evaluate the quality of our algorithm in this context, we entered the PACE 2016 challenge [13] and won the first place in the corresponding sequential competition track. We can therefore conlude that our FlowCutter algorithm finds small, balanced cuts on a wide variety of graphs.

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.

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.