Related papers: Computing Homotopic Shortest Paths Efficiently
The problem of finding the shortest path for a vehicle visiting a given sequence of target points subject to the motion constraints of the vehicle is an important problem that arises in several monitoring and surveillance applications…
The advancement of mobile technologies and the proliferation of map-based applications have enabled a user to access a wide variety of services that range from information queries to navigation systems. Due to the popularity of map-based…
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,…
The current paper deals with the subject of shortest path routing in transportation networks (in terms of travelling time), where the speed in several of the network's roads is a function of the time interval. The main contribution of the…
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…
Clustering is a technique for the analysis of datasets obtained by empirical studies in several disciplines with a major application for biomedical research. Essentially, clustering algorithms are executed by machines aiming at finding…
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…
Bj\"orklund and Husfeldt developed a randomized polynomial time algorithm to solve the shortest two disjoint paths problem. Their algorithm is based on computation of permanents modulo 4 and the isolation lemma. In this paper, we consider…
Here the All-pairs shortest path problem on weighted undirected sparse graphs is being considered. For the problem considered, we propose ``disassembly and assembly of a graph'' algorithm which uses a solution of the problem on a…
The problem of providing meaningful routing directions over road networks is of great importance. In many real-life cases, the fastest route may not be the ideal choice for providing directions in written, spoken text, or for an unfamiliar…
In several important routing contexts it is required to identify a set of routes, each of which optimizes a different criterion. For instance, in the context of vehicle routing, one route would minimize the total distance traveled, while…
The parametric shortest path problem is to find the shortest paths in graph where the edge costs are of the form w_ij+lambda where each w_ij is constant and lambda is a parameter that varies. The problem is to find shortest path trees for…
We study the Short Path Packing problem which asks, given a graph $G$, integers $k$ and $\ell$, and vertices $s$ and $t$, whether there exist $k$ pairwise internally vertex-disjoint $s$-$t$ paths of length at most $\ell$. The problem has…
This paper presents an approximation algorithm for finding a shortest path between two points $s$ and $t$ in a weighted planar subdivision $\PS$. Each face $f$ of $\PS$ is associated with a weight $w_f$, and the cost of travel along a line…
The problem of finding the shortest path in a graph G(V, E) has been widely studied. However, in many applications it is necessary to compute an arbitrary number of them, k. Even though the problem has raised a lot of interest from…
This article provides an overview of the performance and the theoretical complexity of approximate and exact methods for various versions of the shortest path problem. The proposed study aims to improve the resolution of a more general…
This paper is concerned with determining the shortest path for a pursuer aiming to intercept a moving target travelling at a constant speed. To address this challenge, we introduce an efficient mathematical model outlined as an optimal…
In this article, we present an approximation algorithm for solving the Weighted Region Problem amidst a set of $ n $ non-overlapping weighted disks in the plane. For a given parameter $ \varepsilon \in (0,1]$, the length of the approximate…
Given two points in the plane, and a set of "obstacles" given as curves through the plane with assigned weights, we consider the point-separation problem, which asks for the minimum-weight subset of the obstacles separating the two points.…
Through the development of efficient algorithms, data structures and preprocessing techniques, real-world shortest path problems in street networks are now very fast to solve. But in reality, the exact travel times along each arc in the…