Related papers: Reconstructing random graphs from distance queries
The MaxClique problem, finding the largest complete subgraph in an Erd{\"o}s-R{\'e}nyi $G(N,p)$ random graph in the large $N$ limit, is a well-known example of a simple problem for which finding any approximate solution within a factor of…
In this paper, we study the acquaintance time $\AC(G)$ defined for a connected graph $G$. We focus on $\G(n,r,p)$, a random subgraph of a random geometric graph in which $n$ vertices are chosen uniformly at random and independently from…
We give an efficient algorithm to generate a graph from a distribution $\epsilon$-close to $G(n,p)$, in the sense of total variation distance. In particular, if $p$ is represented with $O(\log n)$-bit accuracy, then, with high probability,…
Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph. We show that,…
Graphlets are subgraphs rooted at a fixed vertex. The number of occurrences of graphlets aligned to a particular vertex, called graphlet degree sequence (gds), gives a topological description of the surrounding of the analyzed vertex.…
It is not hard to write a first order formula which is true for a given graph G but is false for any graph not isomorphic to G. The smallest number $(G) of nested quantifiers in a such formula can serve as a measure for the ``first order…
A $k$-deck of a (coloured) graph is a multiset of its induced $k$-vertex subgraphs. Given a graph $G$, when is it possible to reconstruct with high probability a uniformly random colouring of its vertices in $r$ colours from its $k$-deck?…
This paper studies the round complexity of computing the weighted diameter and radius of a graph in the quantum CONGEST model. We present a quantum algorithm that $(1+o(1))$-approximates the diameter and radius with round complexity…
A vertex $v$ of a connected graph $G$ is said to be a boundary vertex of $G$ if for some other vertex $u$ of $G$, no neighbor of $v$ is further away from $u$ than $v$. The boundary $\partial(G)$ of $G$ is the set of all of its boundary…
We consider the problem of reconstructing the intrinsic geometry of a manifold from noisy pairwise distance observations. Specifically, let $M$ denote a diameter 1 d-dimensional manifold and $\mu$ a probability measure on $M$ that is…
Given query access to an undirected graph $G$, we consider the problem of computing a $(1\pm\epsilon)$-approximation of the number of $k$-cliques in $G$. The standard query model for general graphs allows for degree queries, neighbor…
We present a randomized algorithm that computes a constant approximation of a graph's arboricity, using $\tilde{O}(n/\lambda)$ queries to adjacency lists and in the same time bound. Here, $n$ and $\lambda$ denote the number of nodes and the…
Spanners have been shown to be a powerful tool in graph algorithms. Many spanner constructions use a certain type of clustering at their core, where each cluster has small diameter and there are relatively few spanner edges between…
We consider a problem introduced by Feige, Gamarnik, Neeman, R\'acz and Tetali [2020], that of finding a large clique in a random graph $G\sim G(n,\frac{1}{2})$, where the graph $G$ is accessible by queries to entries of its adjacency…
Given a graph $G=(V, E)$ and and a proper labeling $f$ from $V$ to $\{1, ..., n\}$, we define $B(f)$ as the maximum absolute difference between $f(u)$ and $f(v)$ where $(u,v)\in E$. The bandwidth of $G$ is the minimum $B(f)$ for all $f$.…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
We study fundamental graph parameters such as the Diameter and Radius in directed graphs, when distances are measured using a somewhat unorthodox but natural measure: the distance between $u$ and $v$ is the minimum of the shortest path…
We study the richness of the ensemble of graphical structures (i.e., unlabeled graphs) of the one-dimensional random geometric graph model defined by $n$ nodes randomly scattered in $[0,1]$ that connect if they are within the connection…
We study the replacement paths problem in the $\mathsf{CONGEST}$ model of distributed computing. Given an $s$-$t$ shortest path $P$, the goal is to compute, for every edge $e$ in $P$, the shortest-path distance from $s$ to $t$ avoiding $e$.…
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…