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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 compute a minimum cover of point 2transmitters, point k-transmitters, and edge 2-transmitters in a simple polygon. The… (More)

- Undine Leopold
- Discrete & Computational Geometry
- 2017

- Undine Leopold
- 2013

In addition to regular and chiral polyhedra, which have been extensively studied, the vertextransitive polyhedra of higher genus also present an attractive and worthwhile challenge. While the definition is combinatorial, the problem at hand is the realization in Euclidean 3-space as a highly symmetric, non-self-intersecting polyhedron in the more classical… (More)

- Thomas J. Dodd, Mian Ahsan, +18 authors Jason S. Ku
- 2014

We show it is NP-hard to compute a minimum cover of point 2-transmitters, point k-transmitters and edge 2-transmitters in a simple polygon; the point 2transmitter result extends to orthogonal polygons. Introduction. The traditional art gallery problem (AGP) considers placing guards in an art gallery—modeled by a polygon—such that every point in the room can… (More)

- Undine Leopold
- Symmetry
- 2012

This paper describes 4-valent tiling-like structures, called pseudotilings, composed of barrel tiles and apeirogonal pseudotiles in Euclidean 3-space. These (frequently face-to-face) pseudotilings naturally rise in columns above 3-valent plane tilings by convex polygons, such that each column is occupied by stacked congruent barrel tiles or congruent… (More)

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