Related papers: Robustly Guarding Polygons
Despite numerous countermeasures proposed by practitioners and researchers, remote control-flow alteration of programs with memory-safety vulnerabilities continues to be a realistic threat. Guaranteeing that complex software is completely…
We study the design of computationally efficient algorithms with provable guarantees, that are robust to adversarial (test time) perturbations. While there has been an proliferation of recent work on this topic due to its connections to…
With the popularity of drone technologies, aerial photography has become prevalent in many daily scenarios such as environment monitoring, structure inspection, law enforcement etc. A central challenge in this domain is the efficient…
Catering to the incentives of people with limited rationality is a challenging research direction that requires novel paradigms to design mechanisms and approximation algorithms. Obviously strategyproof (OSP) mechanisms have recently…
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…
We present approximation algorithms with O(n^3) processing time for the minimum vertex and edge guard problems in simple polygons. It is improved from previous O(n^4) time algorithms of Ghosh. For simple polygon, there are O(n^3) visibility…
With the introduction of machine learning in high-stakes decision making, ensuring algorithmic fairness has become an increasingly important problem to solve. In response to this, many mathematical definitions of fairness have been…
This paper addresses problems on the robust structural design of complex networks. More precisely, we address the problem of deploying the minimum number of dedicated sensors, i.e., those measuring a single state variable, that ensure the…
This paper is concerned with objective value performance of the scenario approach for robust convex optimization. A novel method is proposed to derive probabilistic bounds for the objective value from scenario programs with a finite number…
We consider the robust version of items selection problem, in which the goal is to choose representatives from a family of sets, preserving constraints on the allowed items' combinations. We prove NP-hardness of the deterministic version,…
Progress in the last decade has brought about significant improvements in the accuracy and speed of SLAM systems, broadening their mapping capabilities. Despite these advancements, long-term operation remains a major challenge, primarily…
As AI advances, copyrighted content faces growing risk of unauthorized use, whether through model training or direct misuse. Building upon invisible adversarial perturbation, recent works developed copyright protections against specific AI…
We consider polynomial approximations of z-bar to better understand the torsional rigidity of polygons. Our main focus is on low degree approximations and associated extremal problems that are analogous to Polya's conjecture for torsional…
This paper studies the robustness of observability of a linear time-invariant system under sensor failures from a computational perspective. To be precise, the problem of determining the minimum number of sensors whose removal can destroy…
Given a simple polygon $\mathcal{P}$ on $n$ vertices, two points $x,y$ in $\mathcal{P}$ are said to be visible to each other if the line segment between $x$ and $y$ is contained in $\mathcal{P}$. The Point Guard Art Gallery problem asks for…
We consider methods for finding a simple polygon of minimum (Min-Area) or maximum (Max-Area) possible area for a given set of points in the plane. Both problems are known to be NP-hard; at the center of the recent CG Challenge, practical…
In this work, we propose a robust optimization approach to mitigate the impact of uncertainties in particle precipitation. Our model incorporates partial differential equations, more particular nonlinear and nonlocal population balance…
Intercepting dynamic objects in uncertain environments involves a significant unresolved challenge in modern robotic systems. Current control approaches rely solely on estimated information, and results lack guarantees of robustness and…
We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…
Motivated by secure wireless networking, we consider the problem of placing fixed localizers that enable mobile communication devices to prove they belong to a secure region that is defined by the interior of a polygon. Each localizer views…