Related papers: Estimating perimeter using graph cuts
We study the problem of detecting local geometry in random graphs. We introduce a model $\mathcal{G}(n, p, d, k)$, where a hidden community of average size $k$ has edges drawn as a random geometric graph on $\mathbb{S}^{d-1}$, while all…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
We study the problem of computing approximate minimum edge cuts by distributed algorithms. We use a standard synchronous message passing model where in each round, $O(\log n)$ bits can be transmitted over each edge (a.k.a. the CONGEST…
Graphlets are induced subgraphs of a large network and are important for understanding and modeling complex networks. Despite their practical importance, graphlets have been severely limited to applications and domains with relatively small…
We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut…
This paper deals with the problem of detecting non-isotropic high-dimensional geometric structure in random graphs. Namely, we study a model of a random geometric graph in which vertices correspond to points generated randomly and…
Many algorithms in machine learning and computational geometry require, as input, the intrinsic dimension of the manifold that supports the probability distribution of the data. This parameter is rarely known and therefore has to be…
A random intersection graph is constructed by independently assigning a subset of a given set of objects $W,$ to each vertex of the vertex set $V$ of a simple graph $G.$ There is an edge between two vertices of $V,$ iff their respective…
In this paper, we consider two fundamental cut approximation problems on large graphs. We prove new lower bounds for both problems that are optimal up to logarithmic factors. The first problem is to approximate cuts in balanced directed…
Graph sparsification is a well-established technique for accelerating graph-based learning algorithms, which uses edge sampling to approximate dense graphs with sparse ones. Because the sparsification error is random and unknown, users must…
In the random geometric graph model $\mathsf{Geo}_d(n,p)$, we identify each of our $n$ vertices with an independently and uniformly sampled vector from the $d$-dimensional unit sphere, and we connect pairs of vertices whose vectors are…
A well-defined distance on the parameter space is key to evaluating estimators, ensuring consistency, and building confidence sets. While there are typically standard distances to adopt in a continuous space, this is not the case for…
In this work we provide a new technique to design fast approximation algorithms for graph problems where the points of the graph lie in a metric space. Specifically, we present a sampling approach for such metric graphs that, using a…
We study the component structure of the random graph $G=G_{n,m,d}$. Here $d=O(1)$ and $G$ is sampled uniformly from ${\mathcal G}_{n,m,d}$, the set of graphs with vertex set $[n]$, $m$ edges and maximum degree at most $d$. If $m=\mu n/2$…
Active contour models based on partial differential equations have proved successful in image segmentation, yet the study of their geometric formulation on arbitrary geometric graphs is still at an early stage. In this paper, we introduce…
The number of triangles in a graph is useful to deduce a plethora of important features of the network that the graph is modeling. However, finding the exact value of this number is computationally expensive. Hence, a number of…
We study the distribution of diameters d of Erd\"os-R\'enyi random graphs with average connectivity c. The diameter d is the maximum among all shortest distances between pairs of nodes in a graph and an important quantity for all dynamic…
An identifying code of a graph is a dominating set which uniquely determines all the vertices by their neighborhood within the code. Whereas graphs with large minimum degree have small domination number, this is not the case for the…
In the distance query model, we are given access to the vertex set of a $n$-vertex graph $G$, and an oracle that takes as input two vertices and returns the distance between these two vertices in $G$. We study how many queries are needed to…
Calculating the diameter of an undirected graph requires quadratic running time under the Strong Exponential Time Hypothesis and this barrier works even against any approximation better than 3/2. For planar graphs with positive edge…