Related papers: Merging discrete Morse vector fields: a case of st…
This work focuses on the development of a non-conforming domain decomposition method for the approximation of PDEs based on weakly imposed transmission conditions: the continuity of the global solution is enforced by a discrete number of…
We contribute an approach to the problem of locally computing sparse connected subgraphs of dense graphs. In this setting, given an edge in a connected graph $G = (V, E)$, an algorithm locally decides its membership in a sparse connected…
We study the computational problem of computing a fair means clustering of discrete vectors, which admits an equivalent formulation as editing a colored matrix into one with few distinct color-balanced rows by changing at most $k$ values.…
Graph coloring is fundamental to distributed computing. We give the first general treatment of the coloring of virtual graphs, where the graph $H$ to be colored is locally embedded within the communication graph $G$. Besides generalizing…
We develop a version of discrete Morse theory for finite regular CW complexes equipped with an auxiliary stratification. The key construction is the halo of a cell, which contains all those faces in the boundary that enter closed…
We propose a simple, projection-based algorithm for clustering mixtures of discrete (Bernoulli) distributions. Unlike previous approaches that rely on coordinate-specific ``combinatorial projections,'' our algorithm is rotationally…
Graph clustering has many important applications in computing, but due to growing sizes of graphs, even traditionally fast clustering methods such as spectral partitioning can be computationally expensive for real-world graphs of interest.…
We propose a novel approach which employs random sampling to generate an accurate non-uniform mesh for numerically solving Partial Differential Equation Boundary Value Problems (PDE-BVP's). From a uniform probability distribution U over a…
In this work, we design a nearly linear time discrete Morse theory based algorithm for computing homology groups of 2-manifolds, thereby establishing the fact that computing homology groups of 2-manifolds is remarkably easy. Unlike previous…
We introduce a graph-theoretic framework based on discrete sheaves to diagnose and localize inconsistencies in preference aggregation. Unlike traditional linearization methods (e.g., HodgeRank), this approach preserves the discrete…
Image vectorization converts raster images into vector graphics composed of regions separated by curves. Typical vectorization methods first define the regions by grouping similar colored regions via color quantization, then approximate…
Motivated by distributed machine learning settings such as Federated Learning, we consider the problem of fitting a statistical model across a distributed collection of heterogeneous data sets whose similarity structure is encoded by a…
Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…
We formulate a simple algorithm for computing global exact symmetries of closed discrete curves in plane. The method is based on a suitable trigonometric interpolation of vertices of the given polyline and consequent computation of the…
Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and…
We study the recently introduced problem of finding dense common subgraphs: Given a sequence of graphs that share the same vertex set, the goal is to find a subset of vertices $S$ that maximizes some aggregate measure of the density of the…
The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of the simplices. Later, stability properties of…
We revisit the problem of secure aggregation of high-dimensional vectors in a two-server system such as Prio. These systems are typically used to aggregate vectors such as gradients in private federated learning, where the aggregate itself…
Targeted color-dots with varying shapes and sizes in images are first exhaustively identified, and then their multiscale 2D geometric patterns are extracted for testing spatial uniformness in a progressive fashion. Based on color theory in…
In this paper, we present a formalization of an algorithm to construct admissible discrete vector fields in the Coq theorem prover taking advantage of the SSReflect library. Discrete vector fields are a tool which has been welcomed in the…