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With the advent of autonomous robots with two- and three-dimensional scanning capabilities, classical visibility-based exploration methods from computational geometry have gained in practical importance. However, real-life laser scanning of…

Computational Geometry · Computer Science 2010-09-28 Sandor P. Fekete , Christiane Schmidt

We study the art gallery problem for opposing half guards: guards that can either see to their left or to their right only. We present art gallery theorems, show that the location of half guards in 2-guardable polygons is not restricted to…

Computational Geometry · Computer Science 2022-07-12 Erik Krohn , Bengt J. Nilsson , 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

In the art gallery problem, we are given a closed polygon $P$, with rational coordinates and an integer $k$. We are asked whether it is possible to find a set (of guards) $G$ of size $k$ such that any point $p\in P$ is seen by a point in…

Computational Geometry · Computer Science 2026-03-18 Lucas Meijer , Tillmann Miltzow

Collaborative 3D object detection exploits information exchange among multiple agents to enhance accuracy of object detection in presence of sensor impairments such as occlusion. However, in practice, pose estimation errors due to imperfect…

Computer Vision and Pattern Recognition · Computer Science 2023-03-06 Yifan Lu , Quanhao Li , Baoan Liu , Mehrdad Dianati , Chen Feng , Siheng Chen , Yanfeng Wang

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

We investigate the problem of using mobile robots equipped with 2D range sensors to optimally guard perimeters or regions, i.e., 1D or 2D sets. Given such a set of arbitrary shape to be guarded, and $k$ mobile sensors where the $i$-th…

Robotics · Computer Science 2020-06-11 Si Wei Feng , Jingjin Yu

Let $P$ be an orthogonal polygon of $n$ vertices, without holes. The Orthogonal Polygon Covering with Squares (OPCS) problem takes as input such an orthogonal polygon $P$ with integral vertex coordinates, and asks to find the minimum number…

Computational Geometry · Computer Science 2024-11-19 Anubhav Dhar , Subham Ghosh , Sudeshna Kolay

Determining if a point is in a polygon or not is used by a lot of applications in computer graphics, computer games and geoinformatics. Implementing this check is error-prone since there are many special cases to be considered. This holds…

Computational Geometry · Computer Science 2017-07-25 Michael Galetzka , Patrick O. Glauner

In this article, the issue of guarding multi-agent systems against a sequence of intruder attacks through mobile heterogeneous guards (guards with different ranges) is discussed. The article makes use of graph theoretic abstractions of such…

Discrete Mathematics · Computer Science 2015-03-17 Waseem Abbas , Sajal Bhatia , Xenofon Koutsoukos

We address recently proposed chromatic versions of the classic Art Gallery Problem. Assume a simple polygon $P$ is guarded by a finite set of point guards and each guard is assigned one of $t$ colors. Such a chromatic guarding is said to be…

Computational Geometry · Computer Science 2014-12-15 Frank Hoffmann , Klaus Kriegel , Max Willert

We consider a generalization of the classical Art Gallery Problem, where instead of a light source, the guards, called $k$-transmitters, model a wireless device with a signal that can pass through at most $k$ walls. We show it is NP-hard to…

Computational Geometry · Computer Science 2020-04-15 Sarah Cannon , Thomas G. Fai , Justin Iwerks , Undine Leopold , Christiane Schmidt

Let an orthogonal polyhedron be the union of a finite set of boxes in $\mathbb R^3$ (i.e., cuboids with edges parallel to the coordinate axes), whose surface is a connected 2-manifold. We study the NP-complete problem of guarding a…

Computational Geometry · Computer Science 2019-10-25 Giovanni Viglietta

This paper investigates a pursuit-evasion problem involving three agents: a pursuer, an evader, and a defender. Cooperative guidance laws are developed for the evader-defender team that guarantee interception of the pursuer by the defender…

Systems and Control · Electrical Eng. & Systems 2025-09-16 Saurabh Kumar , Shashi Ranjan Kumar , Abhinav Sinha

We consider the Coalition Structure Learning (CSL) problem in multi-agent systems, motivated by the existence of coalitions in many real-world systems, e.g., trading platforms and auction systems. In this problem, there is a hidden…

Computer Science and Game Theory · Computer Science 2024-12-17 Yixuan Even Xu , Zhe Feng , Fei Fang

Avoiding collisions is one of the vital tasks for systems of autonomous mobile agents. We focus on the problem of finding continuous coordinated paths for multiple mobile disc agents in a 2-d environment with polygonal obstacles. The…

Artificial Intelligence · Computer Science 2014-02-18 Pavel Janovský , Michal Čáp , Jiří Vokřínek

In any simple polygonal art gallery with n walls, we show that it is possible to place floor(n/2)-1 guards whose range of vision is 180 degrees in such a way that every interior point of the gallery can be seen by one of them, and such that…

Combinatorics · Mathematics 2020-07-09 Daniel Florentino , Ethan Moy , Robert Muth

In this work a robust and scalable cooperative multi-agent searching and tracking framework is proposed. Specifically, we study the problem of cooperative searching and tracking of multiple moving targets by a group of autonomous mobile…

Systems and Control · Electrical Eng. & Systems 2026-02-24 Savvas Papaioannou , Panayiotis Kolios , Theocharis Theocharides , Christos G. Panayiotou , Marios M. Polycarpou

We study the problem of guarding orthogonal art galleries with horizontal mobile guards (alternatively, vertical) and point guards, using "rectangular vision". We prove a sharp bound on the minimum number of point guards required to cover…

Combinatorics · Mathematics 2019-11-07 Ervin Győri , Tamás Róbert Mezei

We address a problem of area protection in graph-based scenarios with multiple agents. The problem consists of two adversarial teams of agents that move in an undirected graph shared by both teams. Agents are placed in vertices of the…

Artificial Intelligence · Computer Science 2017-08-25 Marika Ivanová , Pavel Surynek