We study the complexity of symmetric assembly puzzles: given a collection of simple polygons, can we translate, rotate, and possibly flip them so that their interior-disjoint union is line symmetric? On the negative side, we show that the problem is strongly NP-complete even if the pieces are all polyominos. On the positive side, we show that the problem can be solved in polynomial time if the number of pieces is a fixed constant.

中文翻译：

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对称装配难题很难解决，只有几块

我们研究了对称装配难题的复杂性：给定一个简单多边形的集合，我们是否可以平移，旋转并可能翻转它们，以使它们的内部不相交联合是线对称的？消极的一面，我们表明问题是强烈的NP-完全性的，即使这些碎片都是多氨基酸。从积极的一面，我们表明，如果件数为固定常数，则可以在多项式时间内解决问题。