On the complexity of covering points by guillotine cuts
Delia Garijo, Alberto M\'arquez, Rodrigo I. Silveira
TL;DR
This paper proves that the problem of covering points with the fewest guillotine cuts in the plane is NP-complete, extending previous NP-completeness results to this specific geometric covering problem.
Contribution
It introduces a new NP-completeness proof for covering points with disjoint segments and adapts it to show NP-completeness for guillotine cuts.
Findings
Covering points with guillotine cuts is NP-complete.
The problem remains NP-complete even when restricted to guillotine cuts.
The paper extends NP-completeness results to a new geometric covering problem.
Abstract
We show that the problem of covering a set of points in the plane with a minimum number of guillotine cuts is NP-complete. To that end, first we present a new NP-completeness proof for the problem of covering points with disjoint line segments. Then, we adapt the proof to show that the problem remains NP-complete when the segments are guillotine cuts.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Complexity and Algorithms in Graphs · Advanced Graph Theory Research