Related papers: Multiple-Edge-Fault-Tolerant Approximate Shortest-…
Let $G=(V,E)$ be an $n$-nodes non-negatively real-weighted undirected graph. In this paper we show how to enrich a {\em single-source shortest-path tree} (SPT) of $G$ with a \emph{sparse} set of \emph{auxiliary} edges selected from $E$, in…
Our input is an undirected weighted graph $G = (V,E)$ on $n$ vertices along with a source set $S\subseteq V$. The problem is to preprocess $G$ and build a compact data structure such that upon query $Qu(s,v,f)$ where $(s,v) \in S\times V$…
An \emph{$\alpha$-approximate vertex fault-tolerant distance sensitivity oracle} (\emph{$\alpha$-VSDO}) for a weighted input graph $G=(V, E, w)$ and a source vertex $s \in V$ is the data structure answering an $\alpha$-approximate distance…
The resiliency of a network is its ability to remain \emph{effectively} functioning also when any of its nodes or links fails. However, to reduce operational and set-up costs, a network should be small in size, and this conflicts with the…
Computing \emph{all best swap edges} (ABSE) of a spanning tree $T$ of a given $n$-vertex and $m$-edge undirected and weighted graph $G$ means to select, for each edge $e$ of $T$, a corresponding non-tree edge $f$, in such a way that the…
Given a directed graph $G$ with arbitrary real-valued weights, the single source shortest-path problem (SSSP) asks for, given a source $s$ in $G$, finding a shortest path from $s$ to each vertex $v$ in $G$. A classical SSSP algorithm…
We present an $f$-fault tolerant distance oracle for an undirected weighted graph where each edge has an integral weight from $[1 \dots W]$. Given a set $F$ of $f$ edges, as well as a source node $s$ and a destination node $t$, our oracle…
This paper addresses the problem of designing a sparse {\em fault-tolerant} BFS tree, or {\em FT-BFS tree} for short, namely, a sparse subgraph $T$ of the given network $G$ such that subsequent to the failure of a single edge or vertex, the…
This paper addresses the problem of designing a {\em fault-tolerant} $(\alpha, \beta)$ approximate BFS structure (or {\em FT-ABFS structure} for short), namely, a subgraph $H$ of the network $G$ such that subsequent to the failure of some…
Given an undirected unweighted graph $G$ and a source set $S$ of $|S| = \sigma $ sources, we want to build a data structure which can process the following query {\sc Q}$(s,t,e):$ find the shortest distance from $s$ to $t$ avoiding an edge…
This paper considers a natural fault-tolerant shortest paths problem: for some constant integer $f$, given a directed weighted graph with no negative cycles and two fixed vertices $s$ and $t$, compute (either explicitly or implicitly) for…
Let $s$ denote a distinguished source vertex of a non-negatively real weighted and undirected graph $G$ with $n$ vertices and $m$ edges. In this paper we present two efficient \emph{single-source approximate-distance sensitivity oracles},…
Given an $n$-vertex non-negatively real-weighted graph $G$, whose vertices are partitioned into a set of $k$ clusters, a \emph{clustered network design problem} on $G$ consists of solving a given network design optimization problem on $G$,…
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 {\em breadth-first search (BFS)} spanning trees, and address the problem of designing a sparse {\em fault-tolerant} BFS structure, or {\em FT-BFS } for short, resilient to the failure of up to two edges in the given undirected…
A straightforward dynamic programming method for the single-source shortest paths problem (SSSP) in an edge-weighted directed acyclic graph (DAG) processes the vertices in a topologically sorted order. First, we similarly iterate this…
We consider the Shortest Odd Path problem, where given an undirected graph $G$, a weight function on its edges, and two vertices $s$ and $t$ in $G$, the aim is to find an $(s,t)$-path with odd length and, among all such paths, of minimum…
In the decremental single-source shortest paths (SSSP) problem we want to maintain the distances between a given source node $s$ and every other node in an $n$-node $m$-edge graph $G$ undergoing edge deletions. While its static counterpart…
We design $f$-edge fault-tolerant diameter oracles ($f$-FDOs). We preprocess a given graph $G$ on $n$ vertices and $m$ edges, and a positive integer $f$, to construct a data structure that, when queried with a set $F$ of $|F| \leq f$ edges,…
Let G=(V,E)(|V|=n and |E|=m) be an undirected graph with positive edge weights. Let P_{G}(s, t) be a shortest s-t path in G. Let l be the number of edges in P_{G}(s, t). The \emph{Edge Replacement Path} problem is to compute a shortest s-t…