Related papers: Time Dependent Contraction Hierarchies -- Basic Al…

Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the…

The Primal-Dual (PD) algorithm is widely used in convex optimization to determine saddle points. While the stability of the PD algorithm can be easily guaranteed, strict contraction is nontrivial to establish in most cases. This work…

Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms. In this opinion paper, we provide five main opinions on the virtues of contraction…

Hierarchical decision-making is a natural paradigm for coordinating multi-agent systems in complex environments such as air traffic management. In this paper, we present a bilevel framework for game-theoretic hierarchical routing, where a…

We give a generalized definition of stretch that simplifies the efficient construction of low-stretch embeddings suitable for graph algorithms. The generalization, based on discounting highly stretched edges by taking their $p$-th power for…

Contraction Hierarchies is a successful speedup-technique to Dijkstra's seminal shortest path algorithm that has a convenient trade-off between preprocessing and query times. We investigate a shared-memory parallel implementation that uses…

Multivariate time series forecasting with hierarchical structure is widely used in real-world applications, e.g., sales predictions for the geographical hierarchy formed by cities, states, and countries. The hierarchical time series (HTS)…

We study exact, efficient and practical algorithms for route planning in large road networks. Routing applications often require integrating the current traffic situation, planning ahead with traffic predictions for the future, respecting…

Vehicular Ad Hoc Networks (VANETs) are a cornerstone of intelligent transportation systems, facilitating real-time communication between vehicles and infrastructure. However, the dynamic nature of VANETs introduces significant challenges in…

The widespread use of GPS-enabled devices generates voluminous and continuous amounts of traffic data but analyzing such data for interpretable and actionable insights poses challenges. A hierarchical clustering of the trips has many uses…

Hierarchical matrices can be used to construct efficient preconditioners for partial differential and integral equations by taking advantage of low-rank structures in triangular factorizations and inverses of the corresponding stiffness…

Hierarchical forecasting is a key problem in many practical multivariate forecasting applications - the goal is to simultaneously predict a large number of correlated time series that are arranged in a pre-specified aggregation hierarchy.…

Wireless network topologies change over time and maintaining routes requires frequent updates. Updates are costly in terms of consuming throughput available for data transmission, which is precious in wireless networks. In this paper, we…

Reduced-rank decompositions provide descriptions of the variation among the elements of a matrix or array. In such decompositions, the elements of an array are expressed as products of low-dimensional latent factors. This article presents a…

We consider a recently introduced class of network construction problems where edges of a transportation network need to be constructed by a server (construction crew). The server has a constant construction speed which is much lower than…

In the last decade, there has been a substantial amount of research in finding routing algorithms designed specifically to run on real-world graphs. In 2010, Abraham et al. showed upper bounds on the query time in terms of a graph's highway…

This paper studies the contraction properties of nonlinear differential-algebraic equation (DAE) systems. Specifically we develop scalable techniques for constructing the attraction regions associated with a particular stable equilibrium,…

In this paper we extend to a generic class of piecewise smooth dynamical systems a fundamental tool for the analysis of convergence of smooth dynamical systems: contraction theory. We focus on switched systems satisfying Caratheodory…

Contraction Clustering (RASTER) is a single-pass algorithm for density-based clustering of 2D data. It can process arbitrary amounts of data in linear time and in constant memory, quickly identifying approximate clusters. It also exhibits…

Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results…