Related papers: Polygon Exploration with Time-Discrete Vision
We propose a technique called Rotate-and-Kill for solving the polygon inclusion and circumscribing problems. By applying this technique, we obtain $O(n)$ time algorithms for computing (1) the maximum area triangle in a given $n$-sided…
We consider the problem of time-limited robotic exploration in previously unseen environments where exploration is limited by a predefined amount of time. We propose a novel exploration approach using learning-augmented model-based…
There exist many variants of guarding an orthogonal polygon in an orthogonal fashion: sometimes a guard can see an entire rectangle, or along a staircase, or along an orthogonal path with at most $k$ bends. In this paper, we study all these…
In unknown non-convex environments, such as indoor and underground spaces, deploying a fleet of robots to explore the surroundings while simultaneously searching for and tracking targets of interest to maintain high-precision data…
We investigate the online exploration problem (aka covering) of a short-sighted mobile robot moving in an unknown cellular environment with hexagons and triangles as types of cells. To explore a cell, the robot must enter it. Once inside,…
In this paper, we consider the problem of partitioning a polygon into a set of connected disjoint sub-polygons, each of which covers an area of a specific size. The work is motivated by terrain covering applications in robotics, where the…
There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees,…
One of the earliest and most well known problems in computational geometry is the so-called art gallery problem. The goal is to compute the minimum possible number guards placed on the vertices of a simple polygon in such a way that they…
A fundamental problem in shape matching and geometric similarity is computing the maximum area overlap between two polygons under translation. For general simple polygons, the best-known algorithm runs in $O((nm)^2 \log(nm))$ time [Mount,…
We study the problem of Covering Orthogonal Polygons with Rectangles. For polynomial-time algorithms, the best-known approximation factor is $O(\sqrt{\log n})$ when the input polygon may have holes [Kumar and Ramesh, STOC '99, SICOMP '03],…
Acceleration of algorithms is becoming a crucial problem, if larger data sets are to be processed. Evaluation of algorithms is mostly done by using computational geometry approach and evaluation of computational complexity. However in…
We investigate the problem of optimally assigning a large number of robots (or other types of autonomous agents) to guard the perimeters of closed 2D regions, where the perimeter of each region to be guarded may contain multiple disjoint…
A fundamental class of matrix optimization problems that arise in many areas of science and engineering is that of quadratic optimization with orthogonality constraints. Such problems can be solved using line-search methods on the Stiefel…
The Orthogonal Watchman Route Problem (OWRP) entails the search for the shortest path, known as the watchman route, that a robot must follow within a polygonal environment. The primary objective is to ensure that every point in the…
Moving an autonomous agent through an unknown environment is one of the crucial problems for robotics and network analysis. Therefore, it received a lot of attention in the last decades and was analyzed in many different settings. The graph…
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
This article presents a distributed algorithm for a group of robotic agents with omnidirectional vision to deploy into nonconvex polygonal environments with holes. Agents begin deployment from a common point, possess no prior knowledge of…
In the setting of online algorithms, the input is initially not present but rather arrive one-by-one over time and after each input, the algorithm has to make a decision. Depending on the formulation of the problem, the algorithm might be…
Gaze and face tracking algorithms have traditionally battled a compromise between computational complexity and accuracy; the most accurate neural net algorithms cannot be implemented in real time, but less complex real-time algorithms…
This paper develops an algorithm that guides a multi-robot system in an unknown environment in search of fixed targets. The area to be scanned contains an unknown number of convex obstacles of unknown size and shape. The algorithm covers…