Related papers: Effective Resistances in Non-Expander Graphs
In this paper we consider the problem of testing whether a graph has bounded arboricity. The family of graphs with bounded arboricity includes, among others, bounded-degree graphs, all minor-closed graph classes (e.g. planar graphs, graphs…
We revisit the problem of designing sublinear algorithms for estimating the average degree of an $n$-vertex graph. The standard access model for graphs allows for the following queries: sampling a uniform random vertex, the degree of a…
Given a resistive electrical network, we would like to determine whether all the resistances (edges) in the network are working, and if not, identify which edge (or edges) are faulty. To make this determination, we are allowed to measure…
Given a dynamic network, where edges appear and disappear over time, we are interested in finding sets of edges that have similar temporal behavior and form a dense subgraph. Formally, we define the problem as the enumeration of the maximal…
There has been significant recent interest in graph-based nearest neighbor search methods, many of which are centered on the construction of navigable graphs over high-dimensional point sets. A graph is navigable if we can successfully move…
The area of sublinear algorithms have recently received a lot of attention. In this setting, one has to choose specific access model for the input, as the algorithm does not have time to pre-process or even to see the whole input. A…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
In this paper we study the problem of how resilient networks are to node faults. Specifically, we investigate the question of how many faults a network can sustain so that it still contains a large (i.e. linear-sized) connected component…
We give an improved lower bound of 10/3 on the competitive ratio for the exploration of an undirected, edge-weighted graph with a single agent that needs to return to the starting location after visiting all vertices. We assume that the…
In the Travelling Salesman Problem, every vertex of an edge-weighted graph has to be visited by an agent who traverses the edges of the graph. In this problem, it is usually assumed that the costs of each edge are given in advance, making…
We study which property testing and sublinear time algorithms can be transformed into graph streaming algorithms for random order streams. Our main result is that for bounded degree graphs, any property that is constant-query testable in…
We introduce and investigate a new notion of resilience in graph spanners. Let $S$ be a spanner of a graph $G$. Roughly speaking, we say that a spanner $S$ is resilient if all its point-to-point distances are resilient to edge failures.…
For an increasing monotone graph property $\mP$ the \emph{local resilience} of a graph $G$ with respect to $\mP$ is the minimal $r$ for which there exists of a subgraph $H\subseteq G$ with all degrees at most $r$ such that the removal of…
We investigate the number of maximal independent set queries required to reconstruct the edges of a hidden graph. We show that randomised adaptive algorithms need at least $\Omega(\Delta^2 \log(n / \Delta) / \log \Delta)$ queries to…
Conditional lower bounds for dynamic graph problems has received a great deal of attention in recent years. While many results are now known for the fully-dynamic case and such bounds often imply worst-case bounds for the partially dynamic…
Given a graph $G$, a cost function on the non-edges of $G$, and an integer $d$, the problem of finding a cheapest globally rigid supergraph of $G$ in $\mathbb{R}^d$ is NP-hard for $d\geq 1$. For this problem, which is a common…
The adversarial robustness of Graph Neural Networks (GNNs) has been questioned due to the false sense of security uncovered by strong adaptive attacks despite the existence of numerous defenses. In this work, we delve into the robustness…
Recently, in Refs. \cite{jsj} and \cite{res2}, calculation of effective resistances on distance-regular networks was investigated, where in the first paper, the calculation was based on stratification and Stieltjes function associated with…
The girth of a graph, i.e. the length of its shortest cycle, is a fundamental graph parameter. Unfortunately all known algorithms for computing, even approximately, the girth and girth-related structures in directed weighted $m$-edge and…
In the $k$-edge-connected spanning subgraph ($k$ECSS) problem, our goal is to compute a minimum-cost sub-network that is resilient against up to $k$ link failures: Given an $n$-node $m$-edge graph with a cost function on the edges, our goal…