Related papers: Shortest Paths in Nearly Conservative Digraphs
In this paper, our goal is to characterize two graph classes based on the properties of minimal vertex (edge) separators. We first present a structural characterization of graphs in which every minimal vertex separator is a stable set. We…
Let $A$ and $B$ be disjoint, non-adjacent vertex-sets in an undirected, connected graph $G$, whose vertices are associated with positive weights. We address the problem of identifying a minimum-weight subset of vertices $S\subseteq V(G)$…
Consider a setting where possibly sensitive information sent over a path in a network is visible to every {neighbor} of the path, i.e., every neighbor of some node on the path, thus including the nodes on the path itself. The exposure of a…
The k-distance strong shortest path union cover of a graph is the minimum cardinality among all strong shortest path union cover at distance k of G. In this paper we determine the 2-strong shortest path union cover for certain graphs, also…
The Path Contraction and Cycle Contraction problems take as input an undirected graph $G$ with $n$ vertices, $m$ edges and an integer $k$ and determine whether one can obtain a path or a cycle, respectively, by performing at most $k$ edge…
The shortest path problem in graphs is fundamental to AI. Nearly all variants of the problem and relevant algorithms that solve them ignore edge-weight computation time and its common relation to weight uncertainty. This implies that taking…
We study two popular ways to sketch the shortest path distances of an input graph. The first is distance preservers, which are sparse subgraphs that agree with the distances of the original graph on a given set of demand pairs. Prior work…
The determination of the computational complexity of multi-agent pathfinding on directed graphs (diMAPF) has been an open research problem for many years. While diMAPF has been shown to be polynomial for some special cases, only recently,…
A cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle. An L-cycle cover is a cycle cover in which the length of every cycle is in the set L. We investigate how well L-cycle covers of minimum weight…
Finding a d-regular spanning subgraph (or d-factor) of a graph is easy by Tutte's reduction to the matching problem. By the same reduction, it is easy to find a minimal or maximal d-factor of a graph. However, if we require that the…
A path system $\mathscr{P}$ in a graph $G=(V,E)$ is a collection of paths, with exactly one path between any two vertices in $V$. A path system is said to be consistent if it is closed under subpaths. We say that a path system $\mathscr{P}$…
The composition problem for shortest paths asks the following: given shortest paths on weighted graphs M and N which share a common boundary, find the shortest paths on their union. This problem is a crucial step in any algorithm which uses…
Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R^d. We study the convergence of the shortest path distance in such graphs as the sample size…
We consider the parameterized complexity of the problem of tracking shortest s-t paths in graphs, motivated by applications in security and wireless networks. Given an undirected and unweighted graph with a source s and a destination t,…
In this paper we provide a method of finding possible numbers of shortest paths between two points in a space of compact sets in Euclidean space with Hausdorff distance. We also prove that there cannot be some of the numbers of shortest…
Given an undirected graph G and a set A \subseteq V(G), an A-path is a path in G that starts and ends at two distinct vertices of A with intermediate vertices in V(G) \setminus A. An A-path is called an (A,\ell)-path if the length of the…
Orienting the edges of an undirected graph such that the resulting digraph satisfies some given constraints is a classical problem in graph theory, with multiple algorithmic applications. In particular, an $st$-orientation orients each edge…
Given a graph $G$ then a subgraph $H$ is $isometric$ if, for every pair of vertices $u,v$ of $H$, we have $d_H(u,v) = d_G(u,v)$. We say a graph $G$ is $distance\ preserving\ (dp)$ if it has an isometric subgraph of every possible order up…
A modified version of the Dijkstra algorithm using an inventive contraction hierarchy is proposed. The algorithm considers a directed acyclic graph with a conical or semi-circular structure for which a pair of edges is chosen iteratively…
By a well known theorem of Robbins, a graph $G$ has a strongly connected orientation if and only if $G$ is 2-edge-connected and it is easy to find, in linear time, either a cut edge of $G$ or a strong orientation of $G$. A result of Durand…