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

Customizable Contraction Hierarchies with Turn Costs

We incorporate turn restrictions and turn costs into the route planning algorithm customizable contraction hierarchies (CCH). There are two common ways to represent turn costs and restrictions. The edge-based model expands the network so that road segments become vertices and allowed turns become edges. The compact model keeps intersections as vertices, but associates a turn table with each vertex. Although CCH can be used as is on the edge-based model, the performance of preprocessing and customization is severely affected. While the expanded network is only three times larger, both preprocessing and customization time increase by up to an order of magnitude. In this work, we carefully engineer CCH to exploit different properties of the expanded graph. We reduce the increase in customization time from up to an order of magnitude to a factor of about 3. The increase in preprocessing time is reduced even further. Moreover, we present a CCH variant that works on the compact model, and show that it performs worse than the variant on the edge-based model. Surprisingly, the variant on the edge-based model even uses less space than the one on the compact model, although the compact model was developed to keep the space requirement low

Real-Time Traffic Assignment Using Fast Queries in Customizable Contraction Hierarchies

Given an urban road network and a set of origin-destination (OD) pairs, the traffic assignment problem asks for the traffic flow on each road segment. A common solution employs a feasible-direction method, where the direction-finding step requires many shortest-path computations. In this paper, we significantly accelerate the computation of flow patterns, enabling interactive transportation and urban planning applications. We achieve this by revisiting and carefully engineering known speedup techniques for shortest paths, and combining them with customizable contraction hierarchies. In particular, our accelerated elimination tree search is more than an order of magnitude faster for local queries than the original algorithm, and our centralized search speeds up batched point-to-point shortest paths by a factor of up to 6. These optimizations are independent of traffic assignment and can be generally used for (batched) point-to-point queries. In contrast to prior work, our evaluation uses real-world data for all parts of the problem. On a metropolitan area encompassing more than 2.7 million inhabitants, we reduce the flow-pattern computation for a typical two-hour morning peak from 76.5 to 10.5 seconds on one core, and 4.3 seconds on four cores. This represents a speedup of 18 over the state of the art, and three orders of magnitude over the Dijkstra-based baseline

Comparative Study of Speed-Up Routing Algorithms in Road Networks

We study the problem of finding the shortest distance and the shortest path from one node to another in graphs modeling large road networks. Classical algorithms like Dijkstra and Astar do not have good performance in such networks. In recent years, two new approaches called Contraction Hierarchy and Hub Labeling which use preprocessing to generate auxiliary data to improve the query time performance were proposed, and many variants have followed. These algorithms are very efficient on large networks when a large number of queries is expected. In the literature, these algorithms are called speed-up algorithms. More recently, dynamic routing algorithms have been proposed, such as Customizable Contraction Hierarchy and Dynamic Hierarchical Hub Labeling. These are designed to respond efficiently to edge weight changes resulting from changes in traffic. In this thesis, we present an experimental study of the performance of the above static and dynamic routing algorithms on two different road networks, in terms of travel time and query processing time. Our results show that Customizable Contraction Hierarchy is the best for shortest path query in both the static and dynamic settings, while Hub Labeling is the most efficient in answering shortest distance queries in the static setting. We also show that Dynamic Hub Labeling’s edge weight update operations are inefficient in practice

Targeted Branching for the Maximum Independent Set Problem

Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. In recent years, some of the most successful algorithms for solving this problem are based on the branch-and-bound or branch-and-reduce paradigms. In particular, branch-and-reduce algorithms, which combine branch-and-bound with reduction rules, have been able to achieve substantial results, solving many previously infeasible real-world instances. These results were to a large part achieved by developing new, more practical reduction rules. However, other components that have been shown to have a significant impact on the performance of these algorithms have not received as much attention. One of these is the branching strategy, which determines what vertex is included or excluded in a potential solution. Even now, the most commonly used strategy selects vertices solely based on their degree and does not take into account other factors that contribute to the performance of the algorithm. In this work, we develop and evaluate several novel branching strategies for both branch-and-bound and branch-and-reduce algorithms. Our strategies are based on one of two approaches which are motivated by existing research. They either (1) aim to decompose the graph into two or more connected components which can then be solved independently, or (2) try to remove vertices that hinder the application of a reduction rule which can lead to smaller graphs. Our experimental evaluation on a large set of real-world instances indicates that our strategies are able to improve the performance of the state-of-the-art branch-and-reduce algorithm by Akiba and Iwata. To be more specific, our reduction-based packing branching rule is able to outperform the default branching strategy of selecting a vertex of highest degree on 65% of all instances tested. Furthermore, our decomposition-based strategy based on edge cuts is able to achieve a speedup of 2.29 on sparse networks (1.22 on all instances)