Augmenting a Geometric Matching is $NP$-complete

Tillmann Miltzow

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arXiv · 1206.6360

Augmenting a Geometric Matching is $NP$-complete

Tillmann Miltzow

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Abstract

Given $2n$ points in the plane, it is well-known that there always exists a perfect straight-line non-crossing matching. We show that it is $NP$-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.

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Tillmann Miltzow. 2012-06-27. Augmenting a Geometric Matching is $NP$-complete. https://arxiv.org/abs/1206.6360

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