Engineering Data Reduction for Nested Dissection

Many applications rely on time-intensive matrix operations, such as factorization, which can be sped up significantly for large sparse matrices by interpreting the matrix as a sparse graph and computing a node ordering that minimizes the so-called fill-in. In this paper, we engineer new data reduction rules for the minimum fill-in problem, which significantly reduce the size of the graph while producing an equivalent (or near-equivalent) instance. By applying both new and existing data reduction rules exhaustively before nested dissection, we obtain improved quality and at the same time large improvements in running time on a variety of instances. Our overall algorithm outperforms the state-of-the-art significantly: it not only yields better elimination orders, but it does so significantly faster than previously possible. For example, on road networks, where nested dissection algorithms are typically used as a preprocessing step for shortest path computations, our algorithms are on average six times faster than Metis while computing orderings with less fill-in

PACE Solver Description: Tree Depth with FlowCutter

We describe the FlowCutter submission to the PACE 2020 heuristic tree-depth challenge. The task of the challenge consists of computing an elimination tree of small height for a given graph. At its core our submission uses a nested dissection approach, with FlowCutter as graph bisection algorithm

Faster and better nested dissection orders for Customizable Contraction Hierarchies

Graph partitioning has many applications. We consider the acceleration of shortest path queries in road networks using Customizable Contraction Hierarchies (CCH). It is based on computing a nested dissection order by recursively dividing the road network into parts. Recently, with FlowCutter and Inertial Flow, two flow-based graph bipartitioning algorithms have been proposed for road networks. While FlowCutter achieves high-quality results and thus fast query times, it is rather slow. Inertial Flow is particularly fast due to the use of geographical information while still achieving decent query times. We combine the techniques of both algorithms to achieve more than six times faster preprocessing times than FlowCutter and even faster queries on the Europe road network. We show that, using 16 cores of a shared-memory machine, this preprocessing needs four minutes

Engineering Algorithms for Route Planning in Multimodal Transportation Networks

Practical algorithms for route planning in transportation networks are a showpiece of successful Algorithm Engineering. This has produced many speedup techniques, varying in preprocessing time, space, query performance, simplicity, and ease of implementation. This thesis explores solutions to more realistic scenarios, taking into account, e.g., traffic, user preferences, public transit schedules, and the options offered by the many modalities of modern transportation networks

Using Incremental Many-to-One Queries to Build a Fast and Tight Heuristic for A* in Road Networks

We study exact, efficient, and practical algorithms for route planning applications in large road networks. On the one hand, such algorithms should be able to answer shortest path queries within milliseconds. On the other hand, routing applications often require integrating the current traffic situation, planning ahead with predictions for future traffic, respecting forbidden turns, and many other features depending on the specific application. Therefore, such algorithms must be flexible and able to support a variety of problem variants. In this work, we revisit the A* algorithm to build a simple, extensible, and unified algorithmic framework applicable to many route planning problems. A* has been previously used for routing in road networks. However, its performance was not competitive because no sufficiently fast and tight distance estimation function was available. We present a novel, efficient, and accurate A* heuristic using Contraction Hierarchies, another popular speedup technique. The core of our heuristic is a new Contraction Hierarchies query algorithm called Lazy RPHAST, which can efficiently compute shortest distances from many incrementally provided sources toward a common target. Additionally, we describe A* optimizations to accelerate the processing of low-degree vertices, which are typical in road networks, and present a new pruning criterion for symmetrical bidirectional A*. An extensive experimental study confirms the practicality of our approach for many applications