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Related papers: Robustly Guarding Polygons

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This paper studies the problem of defending (1D and 2D) boundaries against a large number of continuous attacks with a heterogeneous group of defenders. The defender team has perfect information of the attack events within some time (finite…

Robotics · Computer Science 2023-02-21 Si Wei Feng , Jingjin Yu

Guarding a polygon with few guards is an old and well-studied problem in computational geometry. Here we consider the following variant: We assume that the polygon is orthogonal and thin in some sense, and we consider a point $p$ to guard a…

Computational Geometry · Computer Science 2016-04-26 Therese Biedl , Saeed Mehrabi

We provide an O(log log OPT)-approximation algorithm for the problem of guarding a simple polygon with guards on the perimeter. We first design a polynomial-time algorithm for building epsilon-nets of size O(1/epsilon log log 1/epsilon) for…

Computational Geometry · Computer Science 2010-01-26 James King , David Kirkpatrick

We study the Cooperative Guarding problem for polygons with holes in a mobile multi-agents setting. Given a set of agents, initially deployed at a point in a polygon with $n$ vertices and $h$ holes, we require the agents to collaboratively…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-03-01 John Augustine , Srikkanth Ramachandran

It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…

Applications · Statistics 2008-11-01 Xinjia Chen , Kemin Zhou , Jorge L. Aravena

In robust optimization, we would like to find a solution that is immunized against all scenarios that are modeled in an uncertainty set. Which scenarios to include in such a set is therefore of central importance for the tractability of the…

Optimization and Control · Mathematics 2024-10-14 Jamie Fairbrother , Marc Goerigk , Mohammad Khosravi

We propose a refinement of the maxmin approach to robustness. A mechanism's payoff guarantee over an ambiguity set is \emph{robust} if the guarantee is approximately satisfied at priors near the ambiguity set (in the weak topology). We show…

Theoretical Economics · Economics 2026-05-06 Ian Ball , Deniz Kattwinkel

The online caching problem aims to minimize cache misses when serving a sequence of requests under a limited cache size. While naive learning-augmented caching algorithms achieve ideal $1$-consistency, they lack robustness guarantees.…

Data Structures and Algorithms · Computer Science 2025-11-17 Peng Chen , Hailiang Zhao , Jiaji Zhang , Xueyan Tang , Yixuan Wang , Shuiguang Deng

We propose and investigate probabilistic guarantees for the adversarial robustness of classification algorithms. While traditional formal verification approaches for robustness are intractable and sampling-based approaches do not provide…

Machine Learning · Computer Science 2025-11-11 Peter Blohm , Patrick Indri , Thomas Gärtner , Sagar Malhotra

As we seek to deploy machine learning models beyond virtual and controlled domains, it is critical to analyze not only the accuracy or the fact that it works most of the time, but if such a model is truly robust and reliable. This paper…

Machine Learning · Computer Science 2020-07-07 Samuel Henrique Silva , Peyman Najafirad

Optimal control of closed quantum systems is a well studied geometrically elegant set of computational theory and techniques that have proven pivotal in the implementation and understanding of quantum computers. The design of a circuit…

Quantum Physics · Physics 2024-04-29 Johannes Aspman , Vyacheslav Kungurtsev , Jakub Marecek

We present an optimal, linear-time algorithm for the following version of terrain guarding: given a 1.5D terrain and a horizontal line, place the minimum number of guards on the line to see all of the terrain. We prove that the cardinality…

Computational Geometry · Computer Science 2019-06-04 Ovidiu Daescu , Stephan Friedrichs , Hemant Malik , Valentin Polishchuk , Christiane Schmidt

The protection of pathways holds immense significance across various domains, including urban planning, transportation, surveillance, and security. This article introduces a groundbreaking approach to safeguarding pathways by employing…

Robotics · Computer Science 2024-05-27 Hamid Hoorfar , Faraneh Fathi , Sara Moshtaghi Largani , Alireza Bagheri

A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…

Optimization and Control · Mathematics 2012-05-01 Daniel P. Mohr , Ina Stein , Thomas Matzies , Christina A. Knapek

The last decade has seen a number of advances in computationally efficient algorithms for statistical methods subject to robustness constraints. An estimator may be robust in a number of different ways: to contamination of the dataset, to…

Machine Learning · Statistics 2025-09-08 Gautam Kamath

Face recognition algorithms have demonstrated very high recognition performance, suggesting suitability for real world applications. Despite the enhanced accuracies, robustness of these algorithms against attacks and bias has been…

Computer Vision and Pattern Recognition · Computer Science 2020-02-10 Richa Singh , Akshay Agarwal , Maneet Singh , Shruti Nagpal , Mayank Vatsa

We are interested in the problem of guarding simple orthogonal polygons with the minimum number of $ r $-guards. The interior point $ p $ belongs an orthogonal polygon $ P $ is visible from $ r $-guard $ g $, if the minimum area rectangle…

Computational Geometry · Computer Science 2017-09-14 Hamid Hoorfar , Alireza Bagheri

Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…

Numerical Analysis · Mathematics 2020-08-20 Vidhi Zala , Robert M. Kirby , Akil Narayan

Current research on defending against adversarial examples focuses primarily on achieving robustness against a single attack type such as $\ell_2$ or $\ell_{\infty}$-bounded attacks. However, the space of possible perturbations is much…

Machine Learning · Computer Science 2024-10-10 Sihui Dai , Chong Xiang , Tong Wu , Prateek Mittal

The widespread adoption of deep learning models places demands on their robustness. In this paper, we consider the robustness of deep neural networks on videos, which comprise both the spatial features of individual frames extracted by a…

Computer Vision and Pattern Recognition · Computer Science 2020-04-07 Min Wu , Marta Kwiatkowska