Related papers: Convexity Helps Iterated Search in 3D

Owing to the significance of combinatorial search strategies both for academia and industry, the introduction of new techniques is a fast growing research field these days. These strategies have really taken different forms ranging from…

Considering a 2D matrix of positive and negative numbers, how might one draw a rectangle within it whose contents sum higher than all other rectangles'? This fundamental problem, commonly known the maximum rectangle problem or subwindow…

Many real-world tasks such as recommending videos with the kids tag can be reduced to finding most similar vectors associated with hard predicates. This task, filtered vector search, is challenging as prior state-of-the-art graph-based…

There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees,…

Open-vocabulary 3D segmentation enables exploration of 3D spaces using free-form text descriptions. Existing methods for open-vocabulary 3D instance segmentation primarily focus on identifying object-level instances but struggle with…

In this vision paper, we propose a shift in perspective for improving the effectiveness of similarity search. Rather than focusing solely on enhancing the data quality, particularly machine learning-generated embeddings, we advocate for a…

We reexamine fundamental problems from computational geometry in the word RAM model, where input coordinates are integers that fit in a machine word. We develop a new algorithm for offline point location, a two-dimensional analog of sorting…

This work presents an efficient approach for neighbourhood searching in 3D point clouds by combining spatial reordering leveraging Space-Filling Curves (SFC), specifically Morton and Hilbert curves, with a linear Octree implementation. We…

The polygon retrieval problem on points is the problem of preprocessing a set of $n$ points on the plane, so that given a polygon query, the subset of points lying inside it can be reported efficiently. It is of great interest in areas such…

Solving complex planning problems has been a long-standing challenge in computer science. Learning-based subgoal search methods have shown promise in tackling these problems, but they often suffer from a lack of completeness guarantees,…

We revisit Hopcroft's problem and related fundamental problems about geometric range searching. Given $n$ points and $n$ lines in the plane, we show how to count the number of point-line incidence pairs or the number of point-above-line…

Efficient and scalable 3D surface reconstruction from range data remains a core challenge in computer graphics and vision, particularly in real-time and resource-constrained scenarios. Traditional volumetric methods based on…

Sorted Table Search Procedures are the quintessential query-answering tool, with widespread usage that now includes also Web Applications, e.g, Search Engines (Google Chrome) and ad Bidding Systems (AppNexus). Speeding them up, at very…

We consider the problem of reporting convex hull points in an orthogonal range query in two dimensions. Formally, let $P$ be a set of $n$ points in $\mathbb{R}^{2}$. A point lies on the convex hull of a point set $S$ if it lies on the…

Dimensionality reduction techniques map data represented on higher dimensions onto lower dimensions with varying degrees of information loss. Graph dimensionality reduction techniques adopt the same principle of providing latent…

Over the last decade, there have been several data structures that, given a planar subdivision and a probability distribution over the plane, provide a way for answering point location queries that is fine-tuned for the distribution. All…

Projective analysis is an important solution for 3D shape retrieval, since human visual perceptions of 3D shapes rely on various 2D observations from different view points. Although multiple informative and discriminative views are…

Hypergraphs, increasingly utilised for modelling complex and diverse relationships in modern networks, gain much attention representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery is one of the…

One of the challenges in optimization of high dimensional problems is finding appropriate solutions in a way that are as close as possible to the global optima. In this regard, one of the most common phenomena that occurs is the curse of…

This paper presents a practical GPU-accelerated convex hull algorithm and a novel Sorting-based Preprocessing Approach (SPA) for planar point sets. The proposed algorithm consists of two stages: (1) two rounds of preprocessing performed on…