Related papers: Fully Dynamic Algorithms for Graph Spanners via Lo…

Let $G$ be a strongly connected directed graph. We consider the following three problems, where we wish to compute the smallest strongly connected spanning subgraph of $G$ that maintains respectively: the $2$-edge-connected blocks of $G$…

We revisit the classical question of the relationship between the diameter of a graph and its expansion properties. One direction is well understood: expander graphs exhibit essentially the lowest possible diameter. We focus on the reverse…

This paper presents near-optimal deterministic parallel and distributed algorithms for computing $(1+\varepsilon)$-approximate single-source shortest paths in any undirected weighted graph. On a high level, we deterministically reduce this…

A stable cutset in a graph $G$ is a set $S\subseteq V(G)$ such that vertices of $S$ are pairwise non-adjacent and such that $G-S$ is disconnected, i.e., it is both stable (or independent) set and a cutset (or separator). Unlike general…

A flow graph $G=(V,E,s)$ is a directed graph with a distinguished start vertex $s$. The dominator tree $D$ of $G$ is a tree rooted at $s$, such that a vertex $v$ is an ancestor of a vertex $w$ if and only if all paths from $s$ to $w$…

Spectral graph sparsification is a classical tool for reducing graph complexity while preserving Laplacian quadratic forms. In graph neural networks (GNNs), sparsification is often used to accelerate computation while maintaining predictive…

For a pair of positive parameters $D,\chi$, a partition ${\cal P}$ of the vertex set $V$ of an $n$-vertex graph $G = (V,E)$ into disjoint clusters of diameter at most $D$ each is called a $(D,\chi)$ network decomposition, if the supergraph…

Miller et al. \cite{MPVX15} devised a distributed\footnote{They actually showed a PRAM algorithm. The distributed algorithm with these properties is implicit in \cite{MPVX15}.} algorithm in the CONGEST model, that given a parameter $k =…

Motivated by multipath routing, we introduce a multi-connected variant of spanners. For that purpose we introduce the $p$-multipath cost between two nodes $u$ and $v$ as the minimum weight of a collection of $p$ internally vertex-disjoint…

We have a set of processors (or agents) and a set of graph networks defined over some vertex set. Each processor can access a subset of the graph networks. Each processor has a demand specified as a pair of vertices $<u, v>$, along with a…

Despite the wide application of Graph Convolutional Network (GCN), one major limitation is that it does not benefit from the increasing depth and suffers from the oversmoothing problem. In this work, we first characterize this phenomenon…

We study robust and efficient distributed algorithms for building and maintaining distributed data structures in dynamic Peer-to-Peer (P2P) networks. P2P networks are characterized by a high level of dynamicity with abrupt heavy node…

A graph $G$ contains a graph $H$ as an induced minor if $H$ can be obtained from $G$ by vertex deletions and edge contractions. The class of $H$-induced-minor-free graphs generalizes the class of $H$-minor-free graphs, but unlike…

A spanner is a sparse subgraph that approximately preserves the pairwise distances of the original graph. It is well known that there is a smooth tradeoff between the sparsity of a spanner and the quality of its approximation, so long as…

A spanner is a sparse subgraph of a given graph $G$ which preserves distances, measured w.r.t.\ some distance metric, up to a multiplicative stretch factor. This paper addresses the problem of constructing graph spanners w.r.t.\ the group…

Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…

Cuts in graphs are a fundamental object of study, and play a central role in the study of graph algorithms. The problem of sparsifying a graph while approximately preserving its cut structure has been extensively studied and has many…

Many real-world networks are prohibitively large for data retrieval, storage and analysis of all of its nodes and links. Understanding the structure and dynamics of these networks entails creating a smaller representative sample of the full…

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…

Over the past decade, there has been increasing interest in distributed/parallel algorithms for processing large-scale graphs. By now, we have quite fast algorithms -- usually sublogarithmic-time and often $poly(\log\log n)$-time, or even…