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Finding dense subgraphs of a large graph is a standard problem in graph mining that has been studied extensively both for its theoretical richness and its many practical applications. In this paper we introduce a new family of dense…

We present an efficient, trivially parallelizable algorithm to compute offset surfaces of shapes discretized using a dexel data structure. Our algorithm is based on a two-stage sweeping procedure that is simple to implement and efficient,…

A domain decomposition method for the solution of general variable-coefficient elliptic partial differential equations on regular domains is introduced. The method is based on tessellating the domain into overlapping thin slabs or shells,…

Parametrized families of PDEs arise in various contexts such as inverse problems, control and optimization, risk assessment, and uncertainty quantification. In most of these applications, the number of parameters is large or perhaps even…

During the Gaussian Splatting optimization process, the scene's geometry can gradually deteriorate if its structure is not deliberately preserved, especially in non-textured regions such as walls, ceilings, and furniture surfaces. This…

Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…

We present a unified approach for characterizing the boundary of a possibly nonconvex domain. Motivated by the well-known Pascoletti--Serafini method of scalarization, we recast the boundary characterization as a multi-criteria optimization…

We prove a novel method for the embedding of a 3-fold rotationally symmetric sphere-type mesh onto a subset of the plane with 3-fold rotational symmetry. The embedding is free-boundary with the only additional constraint on the image set is…

Recently, Gaussian Splatting (GS) has received a lot of attention in surface reconstruction. However, while 3D objects can be of complex and diverse shapes in the real world, existing GS-based methods only limitedly use a single type of…

We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…

We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…

We propose a novel meshless method to compute harmonic maps and conformal maps for surfaces embedded in the Euclidean 3-space, using point cloud data only. Given a surface, or a point cloud approximation, we simply use the standard cubic…

This paper is concerned with the homogenization of Dirichlet problem of elliptic systems in a bounded, smooth domain of finite type. Both the coefficients of the elliptic operator and the Dirichlet boundary data are assumed to be periodic…

Sphericity and roundness are fundamental measures used for assessing object uniformity in 2D and 3D images. However, using their strict definition makes computation costly. As both 2D and 3D microscopy imaging datasets grow larger, there is…

We examine the use of domain decomposition for potentially more efficient mean curvature flow of surface meshes, whose faces are arbitrary simple polygons. We first test traditional domain decomposition methods with and without overlap of…

In this paper, we define a new metric structure on the shape space of a high genus surface. We introduce a rigorous definition of a shape of a surface and construct a metric based on two energies measuring the area distortion and the angle…

3D Gaussian Splatting reconstructs scenes by starting from a sparse Structure-from-Motion initialization and refining under-reconstructed regions. This process is slow, as it requires multiple densification steps where Gaussians are…

The geometric state of a flat boundary is frequently described using the so-called macroscopic parameters. They are a principal tool for dealing with interfaces at the continuous scale. The paper describes a new method for macroscopic…

An algorithm for the generation of non-uniform unstructured grids on ellipsoidal geometries is described. This technique is designed to generate high quality triangular and polygonal meshes appropriate for general circulation modelling on…

The variance reduction speed of physically-based rendering is heavily affected by the adopted importance sampling technique. In this paper we propose a novel online framework to learn the spatial-varying density model with a single small…