Related papers: To Be Connected, or Not to Be Connected: That is t…
The neighbor connectivity of a graph $G$ is the least number of vertices such that removing their closed neighborhoods from $G$ results in a graph that is disconnected, complete or empty. If a~graph is used to model the topology of an…
Considering a graph with unknown weights, can we find the shortest path for a pair of nodes if we know the minimal Steiner trees associated with some subset of nodes? That is, with respect to a fixed latent decision-making system (e.g., a…
This paper addresses the problem of sparse recovery with graph constraints in the sense that we can take additive measurements over nodes only if they induce a connected subgraph. We provide explicit measurement constructions for several…
Connectivity query processing is a fundamental problem in graph processing. Given an undirected graph and two query vertices, the problem aims to identify whether they are connected via a path. Given frequent edge updates in real graph…
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…
Let $G=(V,E)$ be a strongly biconnected directed graph. In this paper we consider the problem of computing an edge subset $H \subseteq E$ of minimum size such that the directed subgraph $(V,H)$ is strongly biconnected.
Fiber graphs of Gr\"obner bases from contingency tables are important in statistical hypothesis testing, where one studies random walks on these graphs using the Metropolis-Hastings algorithm. The connectivity of the graphs has implications…
Given a connected graph $G$ on $n$ vertices and a positive integer $k\le n$, a subgraph of $G$ on $k$ vertices is called a $k$-subgraph in $G$. We design combinatorial approximation algorithms for finding a connected $k$-subgraph in $G$…
A directed graph G = (V,E) is singly connected if for any two vertices v, u of V, the directed graph G contains at most one simple path from v to u. In this paper, we study different algorithms to find a feasible but necessarily optimal…
A k-tree is either a complete graph on (k+1) vertices or given a k-tree G' with n vertices, a k-tree G with (n+1) vertices can be constructed by introducing a new vertex v and picking a k-clique Q in G' and then joining each vertex u in Q.…
We present a deterministic near-linear time algorithm that computes the edge-connectivity and finds a minimum cut for a simple undirected unweighted graph G with n vertices and m edges. This is the first o(mn) time deterministic algorithm…
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…
Dynamic Connectivity is a fundamental algorithmic graph problem, motivated by a wide range of applications to social and communication networks and used as a building block in various other algorithms, such as the bi-connectivity and the…
We prove three new lower bounds for graph connectivity in the $1$-bit broadcast congested clique model, BCC$(1)$. First, in the KT-$0$ version of BCC$(1)$, in which nodes are aware of neighbors only through port numbers, we show an…
Problems related to finding induced subgraphs satisfying given properties form one of the most studied areas within graph algorithms. Such problems have given rise to breakthrough results and led to development of new techniques both within…
An edge-colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connectivity of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in…
Subgraph counting aims to count occurrences of a template T in a given network G(V, E). It is a powerful graph analysis tool and has found real-world applications in diverse domains. Scaling subgraph counting problems is known to be memory…
Given an edge-weighted graph $G=(V,E)$ and a set $E_0\subset E$, the incremental network design problem with minimum spanning trees asks for a sequence of edges $e'_1,\ldots,e'_T\in E\setminus E_0$ minimizing $\sum_{t=1}^Tw(X_t)$ where…
The shortest path problem is among the most fundamental combinatorial optimization problems to answer reachability queries. It is hard to deter-mine which vertices or edges are visited during shortest path traversals. In this paper, we…
In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…