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arXiv · 1809.02710

The Partition Spanning Forest Problem

Philipp Kindermann·Boris Klemz·Ignaz Rutter·Patrick Schnider·André Schulz
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Abstract

Given a set of colored points in the plane, we ask if there exists a crossing-free straight-line drawing of a spanning forest, such that every tree in the forest contains exactly the points of one color class. We show that the problem is NP-complete, even if every color class contains at most five points, but it is solvable in $O(n^2)$ time when each color class contains at most three points. If we require that the spanning forest is a linear forest, then the problem becomes NP-complete even if every color class contains at most four points.

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Philipp Kindermann, Boris Klemz, Ignaz Rutter, Patrick Schnider, André Schulz. 2018-09-07. The Partition Spanning Forest Problem. https://arxiv.org/abs/1809.02710

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