English

Augmenting a Geometric Matching is $NP$-complete

Computational Complexity 2012-06-28 v1 Computational Geometry

Abstract

Given 2n2n points in the plane, it is well-known that there always exists a perfect straight-line non-crossing matching. We show that it is NPNP-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}
}
R2 v1 2026-06-21T21:26:37.560Z