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In recent years, applications such as real-time simulations, autonomous systems, and video games increasingly demand the processing of complex geometric models under stringent time constraints. Traditional geometric algorithms, including…

Convex hull data structures are fundamental in computational geometry. We study insertion-only data structures, supporting various containment and intersection queries. When $P$ is sorted by $x$- or $y$-coordinate, convex hulls can be…

Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…

Functional constrained optimization is becoming more and more important in machine learning and operations research. Such problems have potential applications in risk-averse machine learning, semisupervised learning, and robust optimization…

Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…

Finding the convex hull is a fundamental problem in computational geometry. Quickhull is a fast algorithm for finding convex hulls. In this paper, we present VQhull, a fast parallel implementation of Quickhull that exploits vector…

Consider the problem of minimizing the sum of a smooth convex function and a separable nonsmooth convex function subject to linear coupling constraints. Problems of this form arise in many contemporary applications including signal…

We consider a general conic mixed-binary set where each homogeneous conic constraint $j$ involves an affine function of independent continuous variables and an epigraph variable associated with a nonnegative function, $f_j$, of common…

Fine-grained visual categorization (FGVC) is an important but challenging task due to high intra-class variances and low inter-class variances caused by deformation, occlusion, illumination, etc. An attention convolutional binary neural…

In this paper we present a novel algorithm for concurrent lock-free internal binary search trees (BST) and implement a Set abstract data type (ADT) based on that. We show that in the presented lock-free BST algorithm the amortized step…

Computationally efficient and automated generation of convex hulls is desirable for high throughput materials discovery of thermodynamically stable multi-species crystal structures. A convex hull genetic algorithm is proposed that uses…

A standard design pattern found in many concurrent data structures, such as hash tables or ordered containers, is alternation of parallelizable sections that incur no data conflicts and critical sections that must run sequentially and are…

Single-linkage clustering is a popular form of hierarchical agglomerative clustering (HAC) where the distance between two clusters is defined as the minimum distance between any pair of points across the two clusters. In single-linkage HAC,…

Chan [JACM, 2010] gave a data structure for maintaining the convex hull of a dynamic set of 3D points under insertions and deletions, supporting extreme-point queries. Subsequent refinements by Kaplan, Mulzer, Roditty, Seiferth, and Sharir…

This paper evaluates several improvements to the memory layout of convex hulls to improve computation times for support point queries. The support point query is a fundamental part of common collision algorithms, and the work presented…

This paper introduces a class of mixed-integer formulations for trained ReLU neural networks. The approach balances model size and tightness by partitioning node inputs into a number of groups and forming the convex hull over the partitions…

We present a convex hull algorithm that is accelerated on commodity graphics hardware. We analyze and identify the hurdles of writing a recursive divide and conquer algorithm on the GPU and divise a framework for representing this class of…

This paper addresses the challenge of Granularity Competition in fine-grained classification tasks, which arises due to the semantic gap between multi-granularity labels. Existing approaches typically develop independent hierarchy-aware…

We propose a new and strengthened Branch-and-Bound (BnB) algorithm for the maximum common (connected) induced subgraph problem based on two new operators, Long-Short Memory (LSM) and Leaf vertex Union Match (LUM). Given two graphs for which…

Finding the coordinate-wise maxima and the convex hull of a planar point set are probably the most classic problems in computational geometry. We consider these problems in the self-improving setting. Here, we have $n$ distributions…