10,432 research outputs found
Engineering Art Galleries
The Art Gallery Problem is one of the most well-known problems in
Computational Geometry, with a rich history in the study of algorithms,
complexity, and variants. Recently there has been a surge in experimental work
on the problem. In this survey, we describe this work, show the chronology of
developments, and compare current algorithms, including two unpublished
versions, in an exhaustive experiment. Furthermore, we show what core
algorithmic ingredients have led to recent successes
Polygon Exploration with Time-Discrete Vision
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 useful accuracy does not allow the robot to scan continuously while in
motion; instead, it has to stop each time it surveys its environment. This
requirement was studied by Fekete, Klein and Nuechter for the subproblem of
looking around a corner, but until now has not been considered in an online
setting for whole polygonal regions.
We give the first algorithmic results for this important algorithmic problem
that combines stationary art gallery-type aspects with watchman-type issues in
an online scenario: We demonstrate that even for orthoconvex polygons, a
competitive strategy can be achieved only for limited aspect ratio A (the ratio
of the maximum and minimum edge length of the polygon), i.e., for a given lower
bound on the size of an edge; we give a matching upper bound by providing an
O(log A)-competitive strategy for simple rectilinear polygons, using the
assumption that each edge of the polygon has to be fully visible from some scan
point.Comment: 28 pages, 17 figures, 2 photographs, 3 tables, Latex. Updated some
details (title, figures and text) for final journal revision, including
explicit assumption of full edge visibilit
Multi-Agent Deployment for Visibility Coverage in Polygonal Environments with Holes
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 the environment, and operate only under line-of-sight sensing and
communication. The objective of the deployment is for the agents to achieve
full visibility coverage of the environment while maintaining line-of-sight
connectivity with each other. This is achieved by incrementally partitioning
the environment into distinct regions, each completely visible from some agent.
Proofs are given of (i) convergence, (ii) upper bounds on the time and number
of agents required, and (iii) bounds on the memory and communication
complexity. Simulation results and description of robust extensions are also
included
Visibility properties of polygons
Two problems dealing with visibility in the interior of a polygon are investigated. We present a linear time algorithm for computing the stair-case visibility polygon from a point inside a simple polygon, which is optimal within a constant factor. We show that the problem of locating the minimum number of 90{dollar}\sp\circ{dollar}-flood-lights to illuminate the interior of a simple polygon is NP-complete. We also discuss the generalization of the above results
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