Jigsaw Puzzles, Edge Matching, and Polyomino Packing: Connections and Complexity

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منابع مشابه

Jigsaw Puzzles, Edge Matching, and Polyomino Packing: Connections and ComplexityA preliminary version of this paper was presented at the Gathering for Gardner 6, Atlanta, March 2004

We show that jigsaw puzzles, edge-matching puzzles, and polyomino packing puzzles are all NP-complete. Furthermore, we show direct equivalences between these three types of puzzles: any puzzle of one type can be converted into an equivalent puzzle of any other type.

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Edge-Matching and Jigsaw Puzzles are Really Hard

We prove the computational intractability of rotating and placing n square tiles into a 1 × n array such that adjacent tiles are compatible—either equal edge colors, as in edge-matching puzzles, or matching tab/pocket shapes, as in jigsaw puzzles. Beyond basic NP-hardness, we prove that it is NPhard even to approximately maximize the number of placed tiles (allowing blanks), while satisfying th...

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In recent work by Mossel and Ross, it was asked how large q has to be for a random jigsaw puzzle with q different shapes of “jigs” to have exactly one solution. The jigs are assumed symmetric in the sense that two jigs of the same type always fit together. They showed that for q = o(n) there are a.a.s. multiple solutions, and for q = ω(n) there is a.a.s. exactly one. The latter bound has since ...

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Even 1×n Edge-Matching and Jigsaw Puzzles are Really Hard

Jigsaw puzzles [9] and edge-matching puzzles [5] are two ancient types of puzzle, going back to the 1760s and 1890s, respectively. Jigsaw puzzles involve fitting together a given set of pieces (usually via translation and rotation) into a desired shape (usually a rectangle), often revealing a known image or pattern. The pieces are typically squares with a pocket cut out of or a tab attached to ...

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Even $1 \times n$ Edge-Matching and Jigsaw Puzzles are Really Hard

We prove the computational intractability of rotating and placing n square tiles into a 1×n array such that adjacent tiles are compatible—either equal edge colors, as in edge-matching puzzles, or matching tab/pocket shapes, as in jigsaw puzzles. Beyond basic NP-hardness, we prove that it is NP-hard even to approximately maximize the number of placed tiles (allowing blanks), while satisfying the...

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ژورنال

عنوان ژورنال: Graphs and Combinatorics

سال: 2007

ISSN: 0911-0119,1435-5914

DOI: 10.1007/s00373-007-0713-4