Computing the obstacle number of a plane graph
Computational Geometry
2011-08-15 v2 Discrete Mathematics
Data Structures and Algorithms
Combinatorics
Abstract
An obstacle representation of a plane graph G is V(G) together with a set of opaque polygonal obstacles such that G is the visibility graph on V(G) determined by the obstacles. We investigate the problem of computing an obstacle representation of a plane graph (ORPG) with a minimum number of obstacles. We call this minimum size the obstacle number of G. First, we show that ORPG is NP-hard by reduction from planar vertex cover, resolving a question posed by [8]. Second, we give a reduction from ORPG to maximum degree 3 planar vertex cover. Since this reduction preserves solution values, it follows that ORPG is fixed parameter tractable (FPT) and admits a polynomial-time approximation scheme (PTAS).
Cite
@article{arxiv.1107.4624,
title = {Computing the obstacle number of a plane graph},
author = {Matthew P. Johnson and Deniz Sarioz},
journal= {arXiv preprint arXiv:1107.4624},
year = {2011}
}
Comments
7 pages, 3 figures