arXiv subjects

Sarah Cannon

Publications and source records attributed to Sarah Cannon.

22 records · Page 2Linked to original sources

arXiv2015

Combinatorics and complexity of guarding polygons with edge and point 2-transmitters

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 2-transmitters, point $k$-transmitters, and edge 2-transmitters in a simple polygon. The point 2-transmitter result extends to orthogonal polygons. In addition, we give necessity and sufficiency results for the number of edge 2-transmitters in general, monotone, orthogonal monotone, and orthogonal polygons.

cs.CG↗

arXiv2012

Hidden Mobile Guards in Simple Polygons

We consider guarding classes of simple polygons using mobile guards (polygon edges and diagonals) under the constraint that no two guards may see each other. In contrast to most other art gallery problems, existence is the primary question: does a specific type of polygon admit some guard set? Types include simple polygons and the subclasses of orthogonal, monotone, and starshaped polygons. Additionally, guards may either exclude or include the endpoints (so-called open and closed guards). We provide a nearly complete set of answers to existence questions of open and closed edge, diagonal, and mobile guards in simple, orthogonal, monotone, and starshaped polygons, with some surprising results. For instance, every monotone or starshaped polygon can be guarded using hidden open mobile (edge or diagonal) guards, but not necessarily with hidden open edge or hidden open diagonal guards.

cs.CG↗

arXiv2012

Conflict-free graph orientations with parity constraints

It is known that every multigraph with an even number of edges has an even orientation (i.e., all indegrees are even). We study parity constrained graph orientations under additional constraints. We consider two types of constraints for a multigraph G=(V,E): (1) an exact conflict constraint is an edge set C in E and a vertex v in V such that C should not equal the set of incoming edges at v; (2) a subset conflict constraint is an edge set C in E and a vertex v in V such that C should not be a subset of incoming edges at v. We show that it is NP-complete to decide whether G has an even orientation with exact or subset conflicts, for all conflict sets of size two or higher. We present efficient algorithms for computing parity constrained orientations with disjoint exact or subset conflict pairs.

cs.CG↗

arXiv2012

Two Hands Are Better Than One (up to constant factors)

We study the difference between the standard seeded model of tile self-assembly, and the "seedless" two-handed model of tile self-assembly. Most of our results suggest that the two-handed model is more powerful. In particular, we show how to simulate any seeded system with a two-handed system that is essentially just a constant factor larger. We exhibit finite shapes with a busy-beaver separation in the number of distinct tiles required by seeded versus two-handed, and exhibit an infinite shape that can be constructed two-handed but not seeded. Finally, we show that verifying whether a given system uniquely assembles a desired supertile is co-NP-complete in the two-handed model, while it was known to be polynomially solvable in the seeded model.

cs.CC↗