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We present an algorithm for recovering planted solutions in two well-known models, the stochastic block model and planted constraint satisfaction problems, via a common generalization in terms of random bipartite graphs. Our algorithm…
Typical areas of application of explicit dynamics are impact, crash test, and most importantly, wave propagation simulations. Due to the numerically highly demanding nature of these problems, efficient automatic mesh generators and…
A fourth-order finite volume embedded boundary (EB) method is presented for the unsteady Stokes equations. The algorithm represents complex geometries on a Cartesian grid using EB, employing a technique to mitigate the "small cut-cell"…
We revisit the generation of balanced octrees for adaptive mesh refinement (AMR) of Cartesian domains with immersed complex geometries. In a recent short note [Hasbestan and Senocak, J. Comput. Phys. vol. 351:473-477 (2017)], we showed that…
Neural rendering with Gaussian splatting has advanced novel view synthesis, and most methods reconstruct surfaces via post-hoc mesh extraction. However, existing methods suffer from two limitations: (i) inaccurate geometry in texture-less…
This paper deals with the discrete counterpart of 2D elliptic model problems rewritten in terms of Boundary Integral Equations. The study is done within the framework of Isogeometric Analysis based on B-splines. In such a context, the…
Computing problems that handle large amounts of data necessitate the use of lossless data compression for efficient storage and transmission. We present a novel lossless universal data compression algorithm that uses parallel computational…
Volume-based reconstruction is usually expensive both in terms of memory consumption and runtime. Especially for sparse geometric structures, volumetric representations produce a huge computational overhead. We present an efficient way to…
We propose a new multi-instance dynamic RGB-D SLAM system using an object-level octree-based volumetric representation. It can provide robust camera tracking in dynamic environments and at the same time, continuously estimate geometric,…
With the emergence of 3D Gaussian Splatting (3DGS), numerous pioneering efforts have been made to address the effective compression issue of massive 3DGS data. 3DGS offers an efficient and scalable representation of 3D scenes by utilizing…
We propose a compressive yet effective mesh representation, Blocked and Patchified Tokenization (BPT), facilitating the generation of meshes exceeding 8k faces. BPT compresses mesh sequences by employing block-wise indexing and patch…
Tree embedding has been a fundamental method in algorithm design with wide applications. We focus on the efficiency of building tree embedding in various computational settings under high-dimensional Euclidean $\mathbb{R}^d$. We devise a…
In biobjective mixed integer linear programs (BOMILPs), two linear objectives are minimized over a polyhedron while restricting some of the variables to be integer. Since many of the techniques for finding or approximating the Pareto set of…
We present a dynamic self-balancing octree data structure that enables efficient neighborhood maintenance in evolving metric spaces, a key challenge in modern machine learning systems. Many learning and generative models operate as…
Small animal PET scanners require high spatial resolution and good sensitivity. To reconstruct high-resolution images in 3D-PET, iterative methods, such as OSEM, are superior to analytical reconstruction algorithms, although their high…
The procedural occupancy function is a flexible and compact representation for creating 3D scenes. For rasterization and other tasks, it is often necessary to extract a mesh that represents the shape. Unbounded scenes with long-range camera…
Binary embedding of high-dimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To…
We propose BS-tree, an in-memory implementation of the B+-tree that adopts the structure of the disk-based index (i.e., a balanced, multiway tree), setting the node size to a memory block that can be processed fast and in parallel using…
The goal of this paper is to introduce a new method in computer-aided geometry of solid modeling. We put forth a novel algebraic technique to evaluate any variadic expression between polyhedral d-solids (d = 2, 3) with regularized operators…
The task of automatically segmenting 3-D surfaces representing boundaries of objects is important for quantitative analysis of volumetric images, and plays a vital role in biomedical image analysis. Recently, graph-based methods with a…