Related papers: Time Dependent Contraction Hierarchies -- Basic Al…
Since the first solutions finding minimally weighted routes in weighted digraphs, a plethora of literature has appeared improving the performance of shortest-path queries for use in real-world applications. In this paper, we detail how an…
We present a new heuristic point-to-point routing algorithm based on contraction hierarchies (CH). Given an epsilon >= 0, we can prove that the length of the path computed by our algorithm is at most (1+epsilon) times the length of the…
We consider the problem of quickly computing shortest paths in weighted graphs given auxiliary data derived in an expensive preprocessing phase. By adding a fast weight-customization phase, we extend Contraction Hierarchies by Geisberger et…
This work establishes the technical fundamentals of a well-tuned Customizable Contraction Hierarchies (CCH) implementation that is simple and elegant. We give a detailed overview of the state of the art of CCH, review recent advances on CCH…
Transit Node Routing (TNR) is a fast and exact distance oracle for road networks. We show several new results for TNR. First, we give a surprisingly simple implementation fully based on Contraction Hierarchies that speeds up preprocessing…
A highly successful approach to route planning in networks (particularly road networks) is to identify a hierarchy in the network that allows faster queries after some preprocessing that basically inserts additional "shortcut"-edges into a…
We study the earliest arrival problem in road networks with static time-dependent functions as arc weights. We propose and evaluate the following simple algorithm: (1) average the travel time in k time windows, (2) compute a shortest…
We study the problem of quickly computing point-to-point shortest paths in massive road networks with traffic predictions. Incorporating traffic predictions into routing allows, for example, to avoid commuter traffic congestions. Existing…
The transport capacity of a communication network can be characterized by the transition from a free-flow state to a congested state. Here, we propose a dynamic routing strategy in complex networks based on hierarchical bypass selections.…
Querying the shortest path between two vertexes is a fundamental operation in a variety of applications, which has been extensively studied over static road networks. However, in reality, the travel costs of road segments evolve over time,…
We present a conceptually clear and algorithmically useful framework for parameterizing the costs of tensor network contraction. Our framework is completely general, applying to tensor networks with arbitrary bond dimensions, open legs, and…
Motivated by the grid search method and Bayesian optimization, we introduce the concept of contractibility and its applications in model-based optimization. First, a basic framework of contraction methods is established to construct a…
Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…
Contraction Hierarchies (CH) (Geisberger et al., 2008) is one of the most widely used algorithms for shortest-path queries on road networks. Compared to Dijkstra's algorithm, CH enables orders of magnitude faster query performance through a…
We successfully contract timetable networks with realistic transfer times. Contraction gradually removes nodes from the graph and adds shortcuts to preserve shortest paths. This reduces query times to 1 ms with preprocessing times around 6…
The present paper is devoted to estimating the speed of convergence towards consensus for a general class of discrete-time multi-agent systems. In the systems considered here, both the topology of the interconnection graph and the weight of…
The contraction cost of a tensor network depends on the contraction order. However, the optimal contraction ordering problem is known to be NP-hard. We show that the linear contraction ordering problem for tree tensor networks admits a…
Contracting tensor networks is often computationally demanding. Well-designed contraction sequences can dramatically reduce the contraction cost. We explore the performance of simulated annealing and genetic algorithms, two common discrete…
Very recently a new algorithm to the nonnegative single-source shortest path problem on road networks has been discovered. It is very cache-efficient, but only on static road networks. We show how to augment it to the time-dependent…
Hierarchical clustering is a popular unsupervised data analysis method. For many real-world applications, we would like to exploit prior information about the data that imposes constraints on the clustering hierarchy, and is not captured by…