Related papers: Worst-case time decremental connectivity and k-edg…
In this note, we present a simple algorithm for computing a \emph{$k$-connectivity certificate} in dynamic graph streams. Our algorithm uses $O(n \log^2 n \cdot \max\{k, \log n \log k\})$ bits of space which improves upon the $O(kn \log^3…
Connectivity (or equivalently, unweighted maximum flow) is an important measure in graph theory and combinatorial optimization. Given a graph $G$ with vertices $s$ and $t$, the connectivity $\lambda(s,t)$ from $s$ to $t$ is defined to be…
Driven by many applications in graph analytics, the problem of computing $k$-edge connected components ($k$-ECCs) of a graph $G$ for a user-given $k$ has been extensively studied recently. In this paper, we investigate the problem of…
We provide a simple new randomized contraction approach to the global minimum cut problem for simple undirected graphs. The contractions exploit 2-out edge sampling from each vertex rather than the standard uniform edge sampling. We…
We present a randomized algorithm for dynamic graph connectivity. With failure probability less than $1/n^c$ (for any constant $c$ we choose), our solution has worst case running time $O(\log^3 n)$ per edge insertion, $O(\log^4 n)$ per edge…
We study graph partitioning problems from a min-max perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main…
We present a deterministic fully-dynamic data structure for maintaining information about the cut-vertices in a graph; i.e. the vertices whose removal would disconnect the graph. Our data structure supports insertion and deletion of edges,…
We present the first sublinear-time algorithm for a distributed message-passing network sto compute its edge connectivity $\lambda$ exactly in the CONGEST model, as long as there are no parallel edges. Our algorithm takes $\tilde…
We show a deterministic algorithm for computing edge connectivity of a simple graph with $m$ edges in $m^{1+o(1)}$ time. Although the fastest deterministic algorithm by Henzinger, Rao, and Wang [SODA'17] has a faster running time of…
This paper considers fully dynamic graph algorithms with both faster worst case update time and sublinear space. The fully dynamic graph connectivity problem is the following: given a graph on a fixed set of n nodes, process an online…
We give the first almost-linear time algorithm for computing the \emph{maximal $k$-edge-connected subgraphs} of an undirected unweighted graph for any constant $k$. More specifically, given an $n$-vertex $m$-edge graph $G=(V,E)$ and a…
In the minimum $k$-cut problem, we want to find the minimum number of edges whose deletion breaks the input graph into at least $k$ connected components. The classic algorithm of Karger and Stein runs in $\tilde O(n^{2k-2})$ time, and…
We present space-efficient algorithms for computing cut vertices in a given graph with $n$ vertices and $m$ edges in linear time using $O(n+\min\{m,n\log \log n\})$ bits. With the same time and using $O(n+m)$ bits, we can compute the…
Motivated by applications in network epidemiology, we consider the problem of determining whether it is possible to delete at most $k$ edges from a given input graph (of small treewidth) so that the resulting graph avoids a set…
Vertex connectivity a classic extensively-studied problem. Given an integer $k$, its goal is to decide if an $n$-node $m$-edge graph can be disconnected by removing $k$ vertices. Although a linear-time algorithm was postulated since 1974…
The \emph{maximal $k$-edge-connected subgraphs} problem is a classical graph clustering problem studied since the 70's. Surprisingly, no non-trivial technique for this problem in weighted graphs is known: a very straightforward…
We study the problem of efficiently answering strong connectivity queries under two vertex failures. Given a directed graph $G$ with $n$ vertices, we provide a data structure with $O(nh)$ space and $O(h)$ query time, where $h$ is the height…
We study deterministic algorithms for computing graph cuts, with focus on two fundamental problems: balanced sparse cut and $k$-vertex connectivity for small $k$ ($k=O(\polylog n)$). Both problems can be solved in near-linear time with…
We show that a problem of deleting a minimum number of vertices from a graph to obtain a graph embeddable on a surface of a given Euler genus is solvable in time $2^{C_g \cdot k^2 \log k} n^{O(1)}$, where $k$ is the size of the deletion…
Boesch and Chen (SIAM J. Appl. Math., 1978) introduced the cut-version of the generalized edge-connectivity, named $k$-edge-connectivity. For any integer $k$ with $2\leq k\leq n$, the {\em $k$-edge-connectivity} of a graph $G$, denoted by…