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arXiv · 1210.3877

Inapproximability of the Smallest Superpolyomino Problem

Andrew Winslow
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Abstract

We consider the \emph{smallest superpolyomino problem}: given a set of colored polyominoes, find the smallest polyomino containing each input polyomino as a subshape. This problem is shown to be NP-hard, even when restricted to a set of polyominoes using a single common color. Moreover, for sets of polyominoes using two or more colors, the problem is shown to be NP-hard to approximate within a $O(n^{1/3-\varepsilon})$-factor for any $\varepsilon > 0$.

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Andrew Winslow. 2012-10-15. Inapproximability of the Smallest Superpolyomino Problem. https://arxiv.org/abs/1210.3877

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