4 research outputs found
Symmetric Assembly Puzzles are Hard, Beyond a Few Pieces
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
Symmetric Assembly Puzzles are Hard, Beyond a Few Pieces
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
Symmetric assembly puzzles are hard, beyond a few pieces
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
Symmetric assembly puzzles are hard, beyond a few pieces
\u3cp\u3eWe 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.\u3c/p\u3