Related papers: Shortest Paths in Graphs with Matrix-Valued Edges:…

The degree centrality of a node, defined as the number of nodes adjacent to it, is often used as a measure of importance of a node to the structure of a network. This metric can be extended to paths in a network, where the degree centrality…

Identifying shortest paths between nodes in a network is a common graph analysis problem that is important for many applications involving routing of resources. An adversary that can manipulate the graph structure could alter traffic…

In this paper we study a variant of the shortest path problem in graphs: given a weighted graph G and vertices s and t, and given a set X of forbidden paths in G, find a shortest s-t path P such that no path in X is a subpath of P. Path P…

Given a graph and a pair of terminals $s$, $t$, the next-to-shortest path problem asks for an $s\!\to \!t$ (simple) path that is shortest among all not shortest $s\!\to \!t$ paths (if one exists). This problem was introduced in 1996, and…

We present the first polynomial time approximation algorithm for computing shortest paths in weighted three-dimensional domains. Given a polyhedral domain $\D$, consisting of $n$ tetrahedra with positive weights, and a real number…

Graph theoretical problems based on shortest paths are at the core of research due to their theoretical importance and applicability. This paper deals with the geodetic number which is a global measure for simple connected graphs and it…

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…

This paper discusses the shortest path problem in a general directed graph with $n$ nodes and $K$ cost scenarios (objectives). In order to choose a solution, the min-max criterion is applied. The min-max version of the problem is hard to…

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…

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…

We state the graph-theoretic computational problem of finding tight paths in a directed, edge-weighted graph, as well as its simplification of finding tight pairs. These problems are motivated by the need of algorithms that find so-called…

We propose a protocol optimization technique that is applicable to both weighted or unweighted graphs. Our aim is to explore by how much a small variation around the Shortest Path or Optimal Path protocols can enhance protocol performance.…

While the shortest path problem has myriad applications, the computational efficiency of suitable algorithms depends intimately on the underlying problem domain. In this paper, we focus on domains where evaluating the edge weight function…

A solution of the $k$ shortest paths problem may output paths that are identical up to a single edge. On the other hand, a solution of the $k$ independent shortest paths problem consists of paths that share neither an edge nor an…

Reconfiguring two shortest paths in a graph means modifying one shortest path to the other by changing one vertex at a time so that all the intermediate paths are also shortest paths. This problem has several natural applications, namely:…

In graph theory, the longest path problem is the problem of finding a simple path of maximum length in a given graph. For some small classes of graphs, the problem can be solved in polynomial time [2, 4], but it remains NP-hard on general…

Vertex connectivity and edge connectivity are fundamental concepts in graph theory that have been widely studied from both structural and algorithmic perspectives. The focus of this paper is on computing these two parameters for graphs…

Computing the shortest path between two given locations in a road network is an important problem that finds applications in various map services and commercial navigation products. The state-of-the-art solutions for the problem can be…

In the graph stream model of computation, an algorithm processes the edges of an input graph in one or more sequential passes while using a memory sublinear in the input size. This model poses significant challenges for constructing long…

The shortest-path distance is a fundamental concept in graph analytics and has been extensively studied in the literature. In many real-world applications, quality constraints are naturally associated with edges in the graphs and finding…