Proceedings ArticleDOI
How many landmark colors are needed to avoid confusion in a polygon
Lawrence H. Erickson,Steven M. LaValle +1 more
- pp 2302-2307
TLDR
An algorithm is provided that solves the first question in polynomial time, and the NP-hardness of the second question is demonstrated.Abstract:
Suppose that two members of a finite point guard set S within a polygon P must be given different colors if their visible regions overlap, and that every point in P is visible from some point in S. The chromatic art gallery problem, introduced in [7], asks for the minimum number of colors required to color any guard set (not necessarily a minimal guard set) of P. We study two related problems. First, given a polygon P and a guard set S of P, can the members of S be efficiently and optimally colored so that no two members of S that have overlapping visibility regions have the same color? Second, given a polygon P and a set of candidate guard locations N, is it possible to efficiently and optimally choose the guard set S ⊆ N that requires the minimum number of colors? We provide an algorithm that solves the first question in polynomial time, and demonstrate the NP-hardness of the second question. Both questions are motivated by common robot tasks such as mapping and surveillance.read more
Citations
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Journal Article
Triangulating a simple polygon in linear time
TL;DR: A deterministic algorithm for triangulating a simple polygon in linear time is given, using the polygon-cutting theorem and the planar separator theorem, whose role is essential in the discovery of new diagonals.
Proceedings Article
On the Chromatic Art Gallery Problem.
TL;DR: It is shown that it is already NP-hard to decide whether two colors suce for covering a polygon with holes, even when arbitrary guard positions are allowed, and a polynomial-time algorithm is given for deciding whether a two-colorable guard set exists.
Posted Content
Complexity of the General Chromatic Art Gallery Problem
TL;DR: It is shown that it is already NP-hard to decide whether two colors suce for covering a polygon with holes, as well as for any xed number k 2 of colors.
Journal ArticleDOI
Watchman routes for lines and line segments
TL;DR: The problem of computing a shortest watchman route for a set of n non-parallel lines in the plane is polynomially tractable, while it becomes NP-hard in 3D.
Journal ArticleDOI
The multi-robot forest coverage for weighted terrain1
Anna Gorbenko,Vladimir Popov +1 more
TL;DR: This paper is devoted to the consideration of efficient algorithms for the problem of the multi-robot forest coverage for weighted terrain and the results of computational experiments with the real-world data, the synthetic terrains with thereal-world weights, and the special hard terrains.
References
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Book
Art gallery theorems and algorithms
TL;DR: In this paper, the authors proposed a visibility algorithm based on three-dimensions and miscellany of the polygons, and showed that minimal guard covers threedimensions of the polygon.
Journal ArticleDOI
Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs
TL;DR: An article of golfing equipment has a golf tee attached to a spring-biassed reel by a length of string which can be aligned with the green or hole and used as an aid in swinging the club face in the correct direction.
Journal Article
Triangulating a simple polygon in linear time
TL;DR: A deterministic algorithm for triangulating a simple polygon in linear time is given, using the polygon-cutting theorem and the planar separator theorem, whose role is essential in the discovery of new diagonals.
Journal ArticleDOI
Triangulating a simple polygon in linear time
TL;DR: In this paper, a deterministic algorithm for triangulating a simple polygon in linear time is presented. But the main tools used are the polygon-cutting theorem, which provides us with a balancing scheme, and the planar separator theorem, whose role is essential in the discovery of new diagonals.