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

Authors:
Erik D. Demaine;Martin L. Demaine
Affiliations:
MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St, 02139, Cambridge, MA, USA;MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St, 02139, Cambridge, MA, USA
Venue:
Graphs and Combinatorics
Year:
2007

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Abstract

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.