Related papers: Decremental Data Structures for Connectivity and D…
This work introduces a novel algorithm for finding the connected components of a graph where the vertices and edges are grouped into sets defining a Set--Based Graph. The algorithm, under certain restrictions on those sets, has the…
A dominating set $D$ of a graph $G$ is a set of vertices such that any vertex in $G$ is in $D$ or its neighbor is in $D$. Enumeration of minimal dominating sets in a graph is one of central problems in enumeration study since enumeration of…
We consider the distributed and parallel construction of low-diameter decompositions with strong diameter for (weighted) graphs and (weighted) graphs that can be separated through $k \in \tilde{O}(1)$ shortest paths. This class of graphs…
We give the first deterministic algorithm that makes sub-quadratic queries to find the global min-cut of a simple graph in the cut query model. Given an $n$-vertex graph $G$, our algorithm makes $\widetilde{O}(n^{5/3})$ queries to compute…
We prove that any $n$-node graph $G$ with diameter $D$ admits shortcuts with congestion $O(\delta D \log n)$ and dilation $O(\delta D)$, where $\delta$ is the maximum edge-density of any minor of $G$. Our proof is simple, elementary, and…
We describe a data structure that maintains the number of triangles in a dynamic undirected graph, subject to insertions and deletions of edges and of degree-zero vertices. More generally it can be used to maintain the number of copies of…
We study \emph{dynamic} algorithms for maintaining spectral vertex sparsifiers of graphs with respect to a set of terminals $T$ of our choice. Such objects preserve pairwise resistances, solutions to systems of linear equations, and energy…
Graphs or networks are a very convenient way to represent data with lots of interaction. Recently, Machine Learning on Graph data has gained a lot of traction. In particular, vertex classification and missing edge detection have very…
We show that the VC-dimension of a graph can be computed in time $n^{\log d+1} d^{O(d)}$, where $d$ is the degeneracy of the input graph. The core idea of our algorithm is a data structure to efficiently query the number of vertices that…
In a strongly connected graph $G = (V,E)$, a cut arc (also called strong bridge) is an arc $e \in E$ whose removal makes the graph no longer strongly connected. Equivalently, there exist $u,v \in V$, such that all $u$-$v$ walks contain $e$.…
Fully dynamic graph is a data structure that (1) supports edge insertions and deletions and (2) answers problem specific queries. The time complexity of (1) and (2) are referred to as the update time and the query time respectively. There…
Next-generation distributed computing networks (e.g., edge and fog computing) enable the efficient delivery of delay-sensitive, compute-intensive applications by facilitating access to computation resources in close proximity to end users.…
{\sc Directed Feedback Vertex Set (DFVS)} is a fundamental computational problem that has received extensive attention in parameterized complexity. In this paper, we initiate the study of a wide generalization, the {\sc ${\cal H}$-free SCC…
Disentangled representation learning has recently attracted a significant amount of attention, particularly in the field of image representation learning. However, learning the disentangled representations behind a graph remains largely…
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…
Cut-based directed graph (digraph) clustering often focuses on finding dense within-cluster or sparse between-cluster connections, similar to cut-based undirected graph clustering methods. In contrast, for flow-based clusterings the edges…
This paper leverages the framework of algorithms-with-predictions to design data structures for two fundamental dynamic graph problems: incremental topological ordering and cycle detection. In these problems, the input is a directed graph…
In the analysis of large-scale network data, a fundamental operation is the comparison of observed phenomena to the predictions provided by null models: when we find an interesting structure in a family of real networks, it is important to…
Edge-coloured directed graphs provide an essential structure for modelling and analysis of complex systems arising in many scientific disciplines (e.g. feature-oriented systems, gene regulatory networks, etc.). One of the fundamental…
One of the most fundamental graph problems is finding a shortest path from a source to a target node. While in its basic forms the problem has been studied extensively and efficient algorithms are known, it becomes significantly harder as…