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arXiv · 1209.5307

Packing identical simple polygons is NP-hard

Sarah R. Allen·John Iacono
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Abstract

Given a small polygon S, a big simple polygon B and a positive integer k, it is shown to be NP-hard to determine whether k copies of the small polygon (allowing translation and rotation) can be placed in the big polygon without overlap. Previous NP-hardness results were only known in the case where the big polygon is allowed to be non-simple. A novel reduction from Planar-Circuit-SAT is presented where a small polygon is constructed to encode the entire circuit.

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Sarah R. Allen, John Iacono. 2012-09-24. Packing identical simple polygons is NP-hard. https://arxiv.org/abs/1209.5307

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