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Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…
Poincar\'e maps play a fundamental role in nonlinear dynamics and chaos theory, offering a means to reduce the dimensionality of continuous dynamical systems by tracking the intersections of trajectories with lower-dimensional section…
A graph $G$ is called $B_k$-VPG, for some constant $k\geq 0$, if it has a string representation on an axis-parallel grid such that each vertex is a path with at most $k$ bends and two vertices are adjacent in $G$ if and only if the…
We investigate the problem of computing the top-$k$ simple shortest paths in weighted digraphs. While the single-pair variant -- finding the top-$k$ simple shortest paths between two specified vertices -- has been extensively studied over…
Most of the existing knowledge graphs are not usually complete and can be complemented by some reasoning algorithms. The reasoning method based on path features is widely used in the field of knowledge graph reasoning and completion on…
In this work we deal with the so-called path convexities, defined over special collections of paths. For example, the collection of the shortest paths in a graph is associated with the well-known geodesic convexity, while the collection of…
Inference and prediction of routes have become of interest over the past decade owing to a dramatic increase in package delivery and ride-sharing services. Given the underlying combinatorial structure and the incorporation of probabilities,…
Geographical routing protocols have several desirable features for use in ad hoc and sensor networks but are susceptible to voids and localization errors. Virtual coordinate systems are an alternative solution to geographically based…
Many robotics applications benefit from being able to compute multiple locally optimal paths in a given configuration space. Examples include path planning for of tethered robots with cable-length constraints, systems involving cables,…
The Restricted Shortest Path (RSP) problem, also known as the Delay-Constrained Least-Cost (DCLC) problem, is an NP-hard bicriteria optimization problem on graphs with $n$ vertices and $m$ edges. In a graph where each edge is assigned a…
Faster pathfinding in time-dependent transport networks is an important and challenging problem in navigation systems. There are two main types of transport networks: road networks for car driving and public transport route network. The…
Route Recommendation (RR) is a core task in route planning within online navigation applications, aiming to recommend the optimal route among candidate routes to users. Industrially, RR adopts the two-stage recall-and-rank framework instead…
The well-known $k$-disjoint path problem ($k$-DPP) asks for pairwise vertex-disjoint paths between $k$ specified pairs of vertices $(s_i, t_i)$ in a given graph, if they exist. The decision version of the shortest $k$-DPP asks for the…
Devising an optimal strategy for navigation in a partially observable environment is one of the key objectives in AI. One of the problem in this context is the Canadian Traveler Problem (CTP). CTP is a navigation problem where an agent is…
We present in this paper several improvements for computing shortest path maps using OpenGL shaders. The approach explores GPU rasterization as a way to propagate optimal costs on a polygonal 2D environment, producing shortest path maps…
The widespread use of graph data in various applications and the highly dynamic nature of today's networks have made it imperative to analyze structural trends in dynamic graphs on a continual basis. The shortest path is a fundamental…
The conditional value-at-risk (CVaR) is a useful risk measure in fields such as machine learning, finance, insurance, energy, etc. When measuring very extreme risk, the commonly used CVaR estimation method of sample averaging does not work…
We introduce stronger notions for approximate single-source shortest-path distances, show how to efficiently compute them from weaker standard notions, and demonstrate the algorithmic power of these new notions and transformations. One…
This paper studies $MPC^{5+}_v$, which is to cover as many vertices as possible in a given graph $G=(V,E)$ by vertex-disjoint $5^+$-paths (i.e., paths each with at least five vertices). $MPC^{5+}_v$ is NP-hard and admits an existing…
Convolutional neural networks (CNNs) have demonstrated their superiority in numerous computer vision tasks, yet their computational cost results prohibitive for many real-time applications such as pedestrian detection which is usually…