English
Related papers

Related papers: Approximating the $k$-Level in Three-Dimensional P…

200 papers

With the proliferation of small aerial vehicles, acquiring close up aerial imagery for high quality reconstruction of complex scenes is gaining importance. We present an adaptive view planning method to collect such images in an automated…

Computer Vision and Pattern Recognition · Computer Science 2019-11-20 Cheng Peng , Volkan Isler

We consider the problem of finding minimum-link rectilinear paths in rectilinear polygonal domains in the plane. A path or a polygon is rectilinear if all its edges are axis-parallel. Given a set $\mathcal{P}$ of $h$ pairwise-disjoint…

Computational Geometry · Computer Science 2015-04-28 Joseph S. B. Mitchell , Valentin Polishchuk , Mikko Sysikaski , Haitao Wang

We study streaming algorithms for the $\ell_p$ subspace approximation problem. Given points $a_1, \ldots, a_n$ as an insertion-only stream and a rank parameter $k$, the $\ell_p$ subspace approximation problem is to find a $k$-dimensional…

Data Structures and Algorithms · Computer Science 2024-06-06 Hossein Esfandiari , Vahab Mirrokni , Praneeth Kacham , David P. Woodruff , Peilin Zhong

In this paper, we study triply periodic surfaces with minimal surface area under a constraint in the volume fraction of the regions (phases) that the surface separates. Using a variational level set method formulation, we present a…

Optimization and Control · Mathematics 2015-06-26 Youngjean Jung , Kevin T. Chu , Salvatore Torquato

We show that there is no $(1+\eps)$-approximation algorithm for the problem of covering points in the plane by minimum number of fat triangles of similar size (with the minimum angle of the triangles being close to 45 degrees). Here, the…

Computational Geometry · Computer Science 2009-08-18 Sariel Har-Peled

We study the complexity of geometric problems on spaces of low fractal dimension. It was recently shown by [Sidiropoulos & Sridhar, SoCG 2017] that several problems admit improved solutions when the input is a pointset in Euclidean space…

Computational Complexity · Computer Science 2017-12-14 Anastasios Sidiropoulos , Kritika Singhal , Vijay Sridhar

Three-dimensional Gaussian Splatting (3DGS) has recently emerged as an efficient representation for novel-view synthesis, achieving impressive visual quality. However, in scenes dominated by large and low-texture regions, common in indoor…

Computer Vision and Pattern Recognition · Computer Science 2025-10-29 Xirui Jin , Renbiao Jin , Boying Li , Danping Zou , Wenxian Yu

A method for detecting and approximating fault lines or surfaces, respectively, or decision curves in two and three dimensions with guaranteed accuracy is presented. Reformulated as a classification problem, our method starts from a set of…

Numerical Analysis · Mathematics 2023-02-17 Matthias Grajewski , Andreas Kleefeld

We develop quantitative algorithmic information bounds for orthogonal projections and distances in the plane. Under mild independence conditions, the distance $|x-y|$ and a projection coordinate $p_e x$ each retain at least half the…

Computational Complexity · Computer Science 2025-09-08 Peter Cholak , Marianna Csörnyei , Neil Lutz , Patrick Lutz , Elvira Mayordomo , D. M. Stull

This paper proposes a new method which builds a simplex based approximation of a $d-1$-dimensional manifold $M$ separating a $d$-dimensional compact set into two parts, and an efficient algorithm classifying points according to this…

Computational Geometry · Computer Science 2018-07-18 Guillaume Deffuant

We study first-order optimization algorithms under the constraint that the descent direction is quantized using a pre-specified budget of $R$-bits per dimension, where $R \in (0 ,\infty)$. We propose computationally efficient optimization…

Machine Learning · Computer Science 2022-08-17 Rajarshi Saha , Mert Pilanci , Andrea J. Goldsmith

Problems on repeated geometric patterns in finite point sets in Euclidean space are extensively studied in the literature of combinatorial and computational geometry. Such problems trace their inspiration to Erd\H{o}s' original work on that…

Computational Geometry · Computer Science 2022-01-03 Aya Bernstine , Yehonatan Mizrahi

We study the problem of minimum enclosing rectangle with outliers, which asks to find, for a given set of $n$ planar points, a rectangle with minimum area that encloses at least $(n-t)$ points. The uncovered points are regarded as outliers.…

Computational Geometry · Computer Science 2021-09-16 Zhengyang Guo , Yi Li

Reduced model spaces, such as reduced basis and polynomial chaos, are linear spaces $V_n$ of finite dimension $n$ which are designed for the efficient approximation of families parametrized PDEs in a Hilbert space $V$. The manifold…

Numerical Analysis · Mathematics 2020-08-04 Albert Cohen , Wolfgang Dahmen , Ron DeVore , Jalal Fadili , Olga Mula , James Nichols

This paper deals with the comparison of planar parallel manipulator architectures based on a multi-objective design optimization approach. The manipulator architectures are compared with regard to their mass in motion and their regular…

Robotics · Computer Science 2010-12-14 Damien Chablat , Stéphane Caro , Raza Ur-Rehman , Philippe Wenger

We develop a new semi-algebraic proof system called Stabbing Planes which formalizes modern branch-and-cut algorithms for integer programming and is in the style of DPLL-based modern SAT solvers. As with DPLL there is only a single rule:…

Computational Complexity · Computer Science 2023-03-20 Paul Beame , Noah Fleming , Russell Impagliazzo , Antonina Kolokolova , Denis Pankratov , Toniann Pitassi , Robert Robere

Pruning neural networks reduces inference time and memory costs. On standard hardware, these benefits will be especially prominent if coarse-grained structures, like feature maps, are pruned. We devise two novel saliency-based methods for…

Machine Learning · Computer Science 2023-09-26 Manuel Nonnenmacher , Thomas Pfeil , Ingo Steinwart , David Reeb

Suppose that there is a ground set which consists of a large number of vectors in a Hilbert space. Consider the problem of selecting a subset of the ground set such that the projection of a vector of interest onto the subspace spanned by…

Information Theory · Computer Science 2015-07-20 Zhenliang Zhang , Yuan Wang , Edwin K. P. Chong , Ali Pezeshki , Louis Scharf

We provide a new lower bound on the number of $(\leq k)$-edges of a set of $n$ points in the plane in general position. We show that for $0 \leq k \leq\lfloor\frac{n-2}{2}\rfloor$ the number of $(\leq k)$-edges is at least $$ E_k(S) \geq…

Combinatorics · Mathematics 2020-07-21 Oswin Aichholzer , Jesús García , David Orden , Pedro Ramos

We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…

Numerical Analysis · Mathematics 2020-05-19 Oleg Balabanov , Anthony Nouy