Related papers: Convexity Helps Iterated Search in 3D
Given a set $P$ of $n$ points in the plane, we consider the problem of computing the number of points of $P$ in a query unit disk (i.e., all query disks have the same radius). We show that the main techniques for simplex range searching in…
The subgraph isomorphism finding problem is a well-studied problem in the field of computer science and graph theory, and it aims to enumerate all instances of a query graph in the respective data graph. In this paper, we propose an…
3D Gaussian Splatting (3DGS) has recently gained significant attention for high-quality and efficient view synthesis, making it widely adopted in fields such as AR/VR, robotics, and autonomous driving. Despite its impressive algorithmic…
In the constrained planarity setting, we ask whether a graph admits a planar drawing that additionally satisfies a given set of constraints. These constraints are often derived from very natural problems; prominent examples are Level…
The convex hull describes the extent or shape of a set of data and is used ubiquitously in computational geometry. Common algorithms to construct the convex hull on a finite set of n points (x,y) range from O(nlogn) time to O(n) time.…
Given a hypergraph $H$, the Planar Support problem asks whether there is a planar graph $G$ on the same vertex set as $H$ such that each hyperedge induces a connected subgraph of $G$. Planar Support is motivated by applications in graph…
Graph pattern matching is a fundamental operation for the analysis and exploration ofdata graphs. In thispaper, we presenta novel approachfor efficiently finding homomorphic matches for hybrid graph patterns, where each pattern edge may be…
Various non-trivial spaces are becoming popular for embedding structured data such as graphs, texts, or images. Following spherical and hyperbolic spaces, more general product spaces have been proposed. However, searching for the best…
In this paper we present new data structures for two extensively studied variants of the orthogonal range searching problem. First, we describe a data structure that supports two-dimensional orthogonal range minima queries in $O(n)$ space…
In the Upper Degree-Constrained Partial Orientation problem we are given an undirected graph $G=(V,E)$, together with two degree constraint functions $d^-,d^+ : V \to \mathbb{N}$. The goal is to orient as many edges as possible, in such a…
In a dynamic retrieval system, documents must be ingested as they arrive, and be immediately findable by queries. Our purpose in this paper is to describe an index structure and processing regime that accommodates that requirement for…
Searching for high-dimensional vector data with high accuracy is an inevitable search technology for various types of data. Graph-based indexes are known to reduce the query time for high-dimensional data. To further improve the query time…
We present an automated and efficient approach for retrieving high-quality CAD models of objects and their poses in a scene captured by a moving RGB-D camera. We first investigate various objective functions to measure similarity between a…
In this paper we present novel algorithmic techniques with a O(H(N)+N/H(N)) time complexity for performing several types of queries and updates on general rooted trees, binary search trees and lists of size N. For rooted trees we introduce…
This paper looks into the problem of grasping unknown objects in a cluttered environment using 3D point cloud data obtained from a range or an RGBD sensor. The objective is to identify graspable regions and detect suitable grasp poses from…
Implicit 3D surface reconstruction of an object from its partial and noisy 3D point cloud scan is the classical geometry processing and 3D computer vision problem. In the literature, various 3D shape representations have been developed,…
Searching recurrent patterns in complex systems with high-dimensional phase spaces is an important task in diverse fields. In the current work, an improved scheme is proposed to accelerate the recently designed variational approach for…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
Efficient structure search is a major challenge in computational materials science. We present a modification of the basin hopping global geometry optimization approach that uses a curvilinear coordinate system to describe global trial…
Graph-based indexing is the dominant approach for approximate nearest neighbor search in vector databases, offering high recall with low latency across billions of vectors. However, in such indices, the edge set of the proximity graph is…