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We study the replacement paths problem in the $\mathsf{CONGEST}$ model of distributed computing. Given an $s$-$t$ shortest path $P$, the goal is to compute, for every edge $e$ in $P$, the shortest-path distance from $s$ to $t$ avoiding $e$.…
Efficiently computing fast paths in large scale dynamic road networks (where dynamic traffic information is known over a part of the network) is a practical problem faced by several traffic information service providers who wish to offer a…
We present a new preprocessing algorithm for embedding the nodes of a given edge-weighted undirected graph into a Euclidean space. The Euclidean distance between any two nodes in this space approximates the length of the shortest path…
The server-centric data centre network architecture can accommodate a wide variety of network topologies. Newly proposed topologies in this arena often require several rounds of analysis and experimentation in order that they might achieve…
This paper develops a structural theory of unique shortest paths in real-weighted graphs. Our main goal is to characterize exactly which sets of node sequences, which we call path systems, can be realized as unique shortest paths in a graph…
Geodesic paths and distances are among the most popular intrinsic properties of 3D surfaces. Traditionally, geodesic paths on discrete polygon surfaces were computed using shortest path algorithms, such as Dijkstra. However, such algorithms…
We present a comparative study of the application of a recently introduced heuristic algorithm to the optimization of transport on three major types of complex networks. The algorithm balances network traffic iteratively by minimizing the…
Planning for Autonomous Unmanned Ground Vehicles (AUGV) is still a challenge, especially in difficult, off-road, critical situations. Automatic planning can be used to reach mission objectives, to perform navigation or maneuvers. Most of…
Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and…
Shortest paths are representative of discrete geodesic distances in graphs, and many descriptors of networks depend on their counting. In multiplex networks, this counting is radically important to quantify the switch between layers and it…
Circuity, the ratio of network distances to straight-line distances, is an important measure of urban street network structure and transportation efficiency. Circuity results from a circulation network's configuration, planning, and…
Given two locations $s$ and $t$ in a road network, a distance query returns the minimum network distance from $s$ to $t$, while a shortest path query computes the actual route that achieves the minimum distance. These two types of queries…
Finding shortest paths in a graph is relevant for numerous problems in computer vision and graphics, including image segmentation, shape matching, or the computation of geodesic distances on discrete surfaces. Traditionally, the concept of…
Shortest paths are not always simple. In planar networks, they can be very different from those with the smallest number of turns - the simplest paths. The statistical comparison of the lengths of the shortest and simplest paths provides a…
The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the…
Real-time motion planning is a vital function of robotic systems. Different from existing roadmap algorithms which first determine the free space and then determine the collision-free path, researchers recently proposed several convex…
Practical global path planning is critical for commercializing cleaning robots working in semi-structured environments. In the literature, global path planning methods for free space usually focus on path length and neglect the traffic rule…
We propose a novel, connectivity-oriented loss function for training deep convolutional networks to reconstruct network-like structures, like roads and irrigation canals, from aerial images. The main idea behind our loss is to express the…
Route choice is often modelled as a two-step procedure in which travellers choose their routes from small sets of promising candidates. Many methods developed to identify such choice sets rely on assumptions about the mechanisms behind the…
Transportation infrastructure, such as road or railroad networks, represent a fundamental component of our civilization. For sustainable planning and informed decision making, a thorough understanding of the long-term evolution of…