Tetravex is NP-complete
Yasuhiko Takenaga, Toby Walsh

TL;DR
This paper proves that deciding whether a Tetravex puzzle has a valid tiling is NP-complete, demonstrating the computational difficulty of the game and relating it to other tiling problems.
Contribution
It establishes the NP-completeness of Tetravex, linking it to other known NP-hard tiling and puzzle problems, and discusses open questions for future research.
Findings
Deciding Tetravex tilings is NP-complete.
Tetravex shares complexity properties with other tiling puzzles.
Raises open questions about infinite versions and puzzle generation.
Abstract
Tetravex is a widely played one person computer game in which you are given unit tiles, each edge of which is labelled with a number. The objective is to place each tile within a by square such that all neighbouring edges are labelled with an identical number. Unfortunately, playing Tetravex is computationally hard. More precisely, we prove that deciding if there is a tiling of the Tetravex board is NP-complete. Deciding where to place the tiles is therefore NP-hard. This may help to explain why Tetravex is a good puzzle. This result compliments a number of similar results for one person games involving tiling. For example, NP-completeness results have been shown for: the offline version of Tetris, KPlumber (which involves rotating tiles containing drawings of pipes to make a connected network), and shortest sliding puzzle problems. It raises a number of open questions.…
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Taxonomy
TopicsCellular Automata and Applications · Computational Geometry and Mesh Generation · Advanced Graph Theory Research
