APUD(1,1) Recognition in Polynomial Time
Computational Geometry
2022-10-11 v1
Abstract
A unit disk graph is the intersection graph of a set of disk of unit radius in the Euclidean plane. In 1998, Breu and Kirkpatrick showed that the recognition problem for unit disk graphs is NP-hard. Given horizontal and vertical lines, an APUD() is a unit disk graph such that each unit disk is centered either on a given horizontal or vertical line. \c{C}a\u{g}{\i}r{\i}c{\i} showed in 2020 that APUD() recognition is NP-hard. In this paper, we show that APUD() recognition is polynomial time solvable.
Cite
@article{arxiv.2210.04090,
title = {APUD(1,1) Recognition in Polynomial Time},
author = {Deniz Ağaoğlu Çağırıcı and Onur Çağırıcı},
journal= {arXiv preprint arXiv:2210.04090},
year = {2022}
}