Related papers: Shotgun reconstruction in the hypercube
In this paper, we consider a weighted generalization of the chromatic number of a Binomial random graph~\(G.\) We equip each edge with a random weight and then colour the vertices in such a way that the absolute colour difference between…
A variational model for reconstruction of damaged color images is studied, in particular in the case where only finitely many colors are admissible for the reconstructed image. An existence result and regularity properties of minimizers are…
Given a graph $G$, the Bell $k$-coloring graph $\mathcal{B}_k(G)$ has vertices given by partitions of $V(G)$ into $k$ independent sets (allowing empty parts), with two partitions adjacent if they differ only in the placement of a single…
Reconfiguration problems ask whether one feasible solution can be transformed into another by a sequence of local moves while maintaining feasibility throughout. For integers $d \geq 1$ and $k \geq d+1$, the Distance Coloring problem asks…
We use a theorem by Ding, Lubetzky and Peres describing the structure of the giant component of random graphs in the strictly supercritical regime, in order to determine the typical size of MAXCUT of $G\sim G\left(n,\frac…
We consider the problem of existence of perfect $2$-colorings (equitable $2$-partitions) of Hamming graphs with given parameters. We start with conditions on parameters of graphs and colorings that are necessary for their existence. Next we…
The b-chromatic number $b(G)$ of a graph $G$ is the maximum $k$ for which $G$ has a proper vertex coloring using $k$ colors such that each color class contains at least one vertex adjacent to a vertex of every other color class. In this…
We investigate the problem of reconstructing a set $P\subseteq \mathbb{R}$ of distinct points, where the only information available about $P$ consists of the distances between some of the pairs of points. More precisely, we examine which…
We formulate and analyze a heterogeneous random hypergraph model, and we provide an achieveability result for recovery of hyperedges from the observed projected graph. We observe a projected graph which combines random hyperedges across all…
Image reconstruction in X ray tomography consists in determining an object from its projections. In many applications such as non destructive testing, we look for an image who has a constant value inside a region (default) and another…
Reconstructing a surface from a point cloud is an underdetermined problem. We use a neural network to study and quantify this reconstruction uncertainty under a Poisson smoothness prior. Our algorithm addresses the main limitations of…
Coloring graphs is an important algorithmic problem in combinatorics with many applications in computer science. In this paper we study coloring tournaments. A chromatic number of a random tournament is of order $\Omega(\frac{n}{\log(n)})$.…
Historical buildings are a treasure and milestone of human cultural heritage. Reconstructing the 3D models of these building hold significant value. The rapid development of neural rendering methods makes it possible to recover the 3D shape…
Markov random fields are used to model high dimensional distributions in a number of applied areas. Much recent interest has been devoted to the reconstruction of the dependency structure from independent samples from the Markov random…
A linearly ordered (LO) $k$-colouring of a hypergraph assigns to each vertex a colour from the set $\{0,1,\ldots,k-1\}$ in such a way that each hyperedge has a unique maximum element. Barto, Batistelli, and Berg conjectured that it is…
We consider random hyperbolic graphs in hyperbolic spaces of any dimension $d+1\geq 2$. We present a rescaling of model parameters that casts the random hyperbolic graph model of any dimension to a unified mathematical framework, leaving…
Refraction is a common physical phenomenon and has long been researched in computer vision. Objects imaged through a refractive object appear distorted in the image as a function of the shape of the interface between the media. This hinders…
We study the problem of bi-chromatic coloring of hypergraphs in the LOCAL distributed model of computation. This problem can easily be solved by a randomized local algorithm with no communication. However, it is not known how to solve it…
In this article, we characterize the strength of the reconstructed singularities and artifacts in a reconstruction formula for limited data spherical Radon transform. Namely, we assume that the data is only available on a closed subset…
An image or volume of interest in positron emission tomography (PET) is reconstructed from pairs of gamma rays emitted from a radioactive substance. Many image reconstruction methods are based on estimation of pixels or voxels on some…