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Dynamic load balancing lies at the heart of distributed caching. Here, the goal is to assign objects (load) to servers (computing nodes) in a way that provides load balancing while at the same time dynamically adjusts to the addition or…
Geosocial reachability queries (\textsc{RangeReach}) determine whether a given vertex in a geosocial network can reach any spatial vertex within a query region. The state-of-the-art 3DReach method answers such queries by encoding graph…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
We present a major revamp of the point-location data structure for general two-dimensional subdivisions via randomized incremental construction, implemented in CGAL, the Computational Geometry Algorithms Library. We can now guarantee that…
Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…
This paper surveys recent analytical and numerical research on linear problems for the integral fractional Laplacian, fractional obstacle problems, and fractional minimal graphs. The emphasis is on the interplay between regularity,…
We propose a distributed computing framework, based on a divide and conquer strategy and hierarchical modeling, to accelerate posterior inference for high-dimensional Bayesian factor models. Our approach distributes the task of…
We analyze the mean cost of the partial match queries in random two-dimensional quadtrees. The method is based on fragmentation theory. The convergence is guaranteed by a coupling argument of Markov chains, whereas the value of the limit is…
Search space is a key consideration for neural architecture search. Recently, Xie et al. (2019) found that randomly generated networks from the same distribution perform similarly, which suggests we should search for random graph…
We introduce a new spatial data structure for high dimensional data called the \emph{approximate principal direction tree} (APD tree) that adapts to the intrinsic dimension of the data. Our algorithm ensures vector-quantization accuracy…
Non-point spatial objects (e.g., polygons, linestrings, etc.) are ubiquitous. We study the problem of indexing non-point objects in memory for range queries and spatial intersection joins. We propose a secondary partitioning technique for…
Understanding associations between paired high-dimensional longitudinal datasets is a fundamental yet challenging problem that arises across scientific domains, including longitudinal multi-omic studies. The difficulty stems from the…
Gaussian Splatting (GS), a recent technique for converting discrete points into continuous spatial representations, has shown promising results in 3D scene modeling and 2D image super-resolution. In this paper, we explore its untapped…
The growing complexity of spatial and structural information in 3D data makes data inspection and visualization a challenging task. We describe a method to create a planar embedding of 3D treelike structures using their skeleton…
Causal discovery is essential for advancing data-driven fields such as scientific AI and data analysis, yet existing approaches face significant time- and space-efficiency bottlenecks when scaling to large graphs. To address this challenge,…
Computing bounded depth decompositions is a bottleneck in many applications of the treedepth parameter. The fastest known algorithm, which is due to Reidl, Rossmanith, S\'{a}nchez Villaamil, and Sikdar [ICALP 2014], runs in…
The Cartesian-tree pattern matching is a recently introduced scheme of pattern matching that detects fragments in a sequential data stream which have a similar structure as a query pattern. Formally, Cartesian-tree pattern matching seeks…
A traversal of a connected graph is a linear ordering of its vertices all of whose initial segments induce connected subgraphs. Traversals, and their refinements such as breadth-first and depth-first traversals, are computed by various…
Advances in generative modeling have recently been adapted to tabular data containing discrete and continuous features. However, generating mixed-type features that combine discrete states with an otherwise continuous distribution in a…
3D Gaussian Splatting has revolutionized neural rendering with real-time performance. However, scaling this approach to large scenes using Level-of-Detail methods faces critical challenges: inefficient serial traversal consuming over 60\%…