Related papers: Convexity Helps Iterated Search in 3D

Hypergraphs, increasingly utilised to model complex and diverse relationships in modern networks, have gained significant attention for representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery…

Hybrid queries combining high-dimensional vector similarity search with spatio-temporal filters are increasingly critical for modern retrieval-augmented generation (RAG) systems. Existing systems typically handle these workloads by nesting…

We revisit the classic problem of simplex range searching and related problems in computational geometry. We present a collection of new results which improve previous bounds by multiple logarithmic factors that were caused by the use of…

In this paper, we first consider the subpath convex hull query problem: Given a simple path $\pi$ of $n$ vertices, preprocess it so that the convex hull of any query subpath of $\pi$ can be quickly obtained. Previously, Guibas, Hershberger,…

Embedding models can generate high-dimensional vectors whose similarity reflects semantic affinities. Thus, accurately and timely retrieving those vectors in a large collection that are similar to a given query has become a critical…

A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More…

This paper presents a novel method for real-time 3D navigation in large-scale, complex environments using a hierarchical 3D visibility graph (V-graph). The proposed algorithm addresses the computational challenges of V-graph construction…

We present a novel spatial hashing based data structure to facilitate 3D shape analysis using convolutional neural networks (CNNs). Our method well utilizes the sparse occupancy of 3D shape boundary and builds hierarchical hash tables for…

A graph $G=(V,E)$ is a support of a hypergraph $H=(V,S)$ if every hyperedge induces a connected subgraph in $G$. Supports are used for certain types of hypergraph visualizations. In this paper we consider visualizing spatial hypergraphs,…

Anytime heuristic search algorithms try to find a (potentially suboptimal) solution as quickly as possible and then work to find better and better solutions until an optimal solution is obtained or time is exhausted. The most widely-known…

A hypergraph is a generalization of a graph, in which a hyperedge can connect multiple vertices, modeling complex relationships involving multiple vertices simultaneously. Hypergraph pattern matching, which is to find all isomorphic…

Spatial data is ubiquitous. Massive amounts of data are generated every day from a plethora of sources such as billions of GPS-enabled devices (e.g., cell phones, cars, and sensors), consumer-based applications (e.g., Uber and Strava), and…

Prune-and-search is an important paradigm for solving many important geometric problems. We show that the general prune-and-search technique can be implemented where the objects are given in read-only memory. As examples we consider…

Spatial data structures allow to make efficient queries on Geographical Information Systems (GIS). Spatial queries involve the geometry of the data, such as points, lines, or polygons. For instance, a spatial query could poll for the…

We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…

LiDAR-based place recognition serves as a crucial enabler for long-term autonomy in robotics and autonomous driving systems. Yet, prevailing methodologies relying on handcrafted feature extraction face dual challenges: (1) Inconsistent…

Visual design tasks often involve tuning many design parameters. For example, color grading of a photograph involves many parameters, some of which non-expert users might be unfamiliar with. We propose a novel user-in-the-loop optimization…

Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex…

We introduce a new method that efficiently computes a set of viewpoints and trajectories for high-quality 3D reconstructions in outdoor environments. Our goal is to automatically explore an unknown area, and obtain a complete 3D scan of a…

Nearest neighbor search is a fundamental data structure problem with many applications in machine learning, computer vision, recommendation systems and other fields. Although the main objective of the data structure is to quickly report…