Augmenting a Geometric Matching is $NP$-complete
Computational Complexity
2012-06-28 v1 Computational Geometry
Abstract
Given points in the plane, it is well-known that there always exists a perfect straight-line non-crossing matching. We show that it is -complete to decide if a partial matching can be augmented to a perfect one, via a reduction from 1-in-3-SAT. This result also holds for bichromatic matchings.
Keywords
Cite
@article{arxiv.1206.6360,
title = {Augmenting a Geometric Matching is $NP$-complete},
author = {Tillmann Miltzow},
journal= {arXiv preprint arXiv:1206.6360},
year = {2012}
}