相关论文: Reachability Preservers: New Extremal Bounds and A…

In the classical survivable network design problem (SNDP), we are given an undirected graph $G=(V,E)$ with costs on edges and a connectivity requirement $k(s,t)$ for each pair of vertices. The goal is to find a minimum-cost subgraph…

Majority of the existing graph neural networks (GNN) learn node embeddings that encode their local neighborhoods but not their positions. Consequently, two nodes that are vastly distant but located in similar local neighborhoods map to…

A unit disk graph is the intersection graph of n congruent disks in the plane. Dominating sets in unit disk graphs are widely studied due to their application in wireless ad-hoc networks. Because the minimum dominating set problem for unit…

A temporal graph is a dynamic graph where every edge is assigned a set of integer time labels that indicate at which discrete time step the edge is available. In this paper, we study how changes of the time labels, corresponding to delays…

We study the classical Node-Disjoint Paths (NDP) problem: given an $n$-vertex graph $G$ and a collection $M=\{(s_1,t_1),\ldots,(s_k,t_k)\}$ of pairs of vertices of $G$ called demand pairs, find a maximum-cardinality set of node-disjoint…

We live in a world increasingly dominated by networks -- communications, social, information, biological etc. A central attribute of many of these networks is that they are dynamic, that is, they exhibit structural changes over time. While…

In this paper, we study the Minimum Weight Pairwise Distance Preservers (MWPDP) problem. Consider a positively weighted undirected/directed connected graph $G = (V, E, c)$ and a subset $P$ of pairs of vertices, also called demand pairs. A…

Given a directed graph $G = (V,E)$, undergoing an online sequence of edge deletions with $m$ edges in the initial version of $G$ and $n = |V|$, we consider the problem of maintaining all-pairs shortest paths (APSP) in $G$. Whilst this…

For a connected graph $G$ of order at least $2$ and $S\subseteq V(G)$, the \emph{Steiner distance} $d_G(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. In this paper, we…

A hypergraph spectral sparsifier of a hypergraph $G$ is a weighted subgraph $H$ that approximates the Laplacian of $G$ to a specified precision. Recent work has shown that similar to ordinary graphs, there exist $\widetilde{O}(n)$-size…

Temporal networks are a class of time-varying networks, which change their topology according to a given time-ordered sequence of static networks (known as subsystems). This paper investigates the reachability and controllability of…

An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…

The notion of vertex sparsification is introduced in \cite{M}, where it was shown that for any graph $G = (V, E)$ and a subset of $k$ terminals $K \subset V$, there is a polynomial time algorithm to construct a graph $H = (K, E_H)$ on just…

We study the family of intersection graphs of low density objects in low dimensional Euclidean space. This family is quite general, and includes planar graphs. We prove that such graphs have small separators. Next, we present efficient…

For the well-known Survivable Network Design Problem (SNDP) we are given an undirected graph $G$ with edge costs, a set $R$ of terminal vertices, and an integer demand $d_{s,t}$ for every terminal pair $s,t\in R$. The task is to compute a…

$\newcommand{\eps}{\varepsilon}$ In this paper, we consider two important problems defined on finite metric spaces, and provide efficient new algorithms and approximation schemes for these problems on inputs given as graph shortest path…

Emerging reconfigurable optical communication technologies allow to enhance datacenter topologies with demand-aware links optimized towards traffic patterns. This paper studies the algorithmic problem of jointly optimizing topology and…

We consider the problem of dominating set-based virtual backbone used for routing in asymmetric wireless ad-hoc networks. These networks have non-uniform transmission ranges and are modeled using the well-established disk graphs. The…

Extremal graph theory studies the maximum or minimum number of subgraphs isomorphic to a prescribed graph under given constraints. \textit{Localization} has recently emerged as a framework that refines such problems by assigning extremal…

We present a general framework of designing efficient dynamic approximate algorithms for optimization on undirected graphs. In particular, we develop a technique that, given any problem that admits a certain notion of vertex sparsifiers,…