Related papers: A Simple Algorithm For Replacement Paths Problem
Let $\mathcal{P}$ be a polygonal domain of $h$ holes and $n$ vertices. We study the problem of constructing a data structure that can compute a shortest path between $s$ and $t$ in $\mathcal{P}$ under the $L_1$ metric for any two query…
We consider the problem of finding a maximum size triangle-free $2$-matching in a graph $G=(V,E)$. A (simple) $2$-matching is any subset of the edges such that each vertex is incident to at most two edges from the subset. The first…
In this paper, we address the numerical solution of the Optimal Transport Problem on undirected weighted graphs, taking the shortest path distance as transport cost. The optimal solution is obtained from the long-time limit of the gradient…
Given a road network modelled as a planar straight-line graph $G=(V,E)$ with $|V|=n$, let $(u,v)\in V\times V$, the shortest path (distance) between $u,v$ is denoted as $\delta_G(u,v)$. Let $\delta(G)=\max_{(u,v)}\delta_G(u,v)$, for…
In this work, we follow the current trend on temporal graph realization, where one is given a property P and the goal is to determine whether there is a temporal graph, that is, a graph where the edge set changes over time, with property P…
Very recently a new algorithm to the nonnegative single-source shortest path problem on road networks has been discovered. It is very cache-efficient, but only on static road networks. We show how to augment it to the time-dependent…
Consider the following distance query for an $n$-node graph $G$ undergoing edge insertions and deletions: given two sets of nodes $I$ and $J$, return the distances between every pair of nodes in $I\times J$. This query is rather general and…
We study dynamic $(1+\epsilon)$-approximation algorithms for the all-pairs shortest paths problem in unweighted undirected $n$-node $m$-edge graphs under edge deletions. The fastest algorithm for this problem is a randomized algorithm with…
The problem of finding, in an edge-weighted bidirected graph $G=(V,E)$, a cycle with minimum mean weight of its edges generalizes similar problems for both directed and undirected graphs. (The problem is considered in two variants: for the…
Given an undirected graph $G=(V,E)$, vertices $s,t\in V$, and an integer $k$, Tracking Shortest Paths requires deciding whether there exists a set of $k$ vertices $T\subseteq V$ such that for any two distinct shortest paths between $s$ and…
Let G=(V,E) be a connected graph, where V and E represent, respectively, the node-set and the edge-set. Besides, let Q \subseteq V be a set of terminal nodes, and r \in Q be the root node of the graph. Given a weight c_{ij} \in \mathbb{N}…
How efficiently can we find an unknown graph using distance or shortest path queries between its vertices? Let $G = (V,E)$ be an unweighted, connected graph of bounded degree. The edge set $E$ is initially unknown, and the graph can be…
For a given graph $G=(V,\, E)$ with a terminal set $S$ and a selected root $r\in S$, a positive integer cost and a delay on every edge and a delay constraint $D\in Z^{+}$, the shallow-light Steiner tree (\emph{SLST}) problem is to compute a…
The approximate single-source shortest-path problem is as follows: given a graph with nonnegative edge weights and a designated source vertex $s$, return estimates of the distances from~$s$ to each other vertex such that the estimate falls…
We study an "above guarantee" version of the {\sc Longest Path} problem in directed graphs: We are given a graph $G$, two vertices $s$ and $t$ of $G$, and a non-negative integer $k$, and the objective is to determine whether $G$ contains a…
We give a polynomial-time algorithm that, with input a graph $G$ and two vertices $u,v$ of $G$, decides whether there is an induced $uv$-path that is longer than the shortest $uv$-path.
This paper details a new algorithm to solve the shortest path problem in valued graphs. Its complexity is $O(D \log v)$ where $D$ is the graph diameter and $v$ its number of vertices. This complexity has to be compared to the one of the…
We consider a generalized version of the (weighted) one-center problem on graphs. Given an undirected graph $G$ of $n$ vertices and $m$ edges and a positive integer $k\leq n$, the problem aims to find a point in $G$ so that the maximum…
The maximum/minimum bisection problems are, given an edge-weighted graph, to find a bipartition of the vertex set into two sets whose sizes differ by at most one, such that the total weight of edges between the two sets is…
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…