TL;DR
This paper proves that determining solvability of Shisen-Sho boards is NP-complete and introduces an efficient algorithm to test tile playability, combining it with existing methods to solve Mahjong Solitaire and Shisen-Sho puzzles.
Contribution
It provides a simple proof of NP-completeness for Shisen-Sho solvability and develops an efficient algorithm for tile playability testing integrated with existing solving techniques.
Findings
Determined Shisen-Sho solvability is NP-complete
Developed a logarithmic-time algorithm for tile playability
Sampled various game layouts for solvability analysis
Abstract
We give a simple proof of that determining solvability of Shisen-Sho boards is NP-complete. Furthermore, we show that under realistic assumptions, one can compute in logarithmic time if two tiles form a playable pair. We combine an implementation of the algoritm to test playability of pairs with my earlier algorithm to solve Mahjong Solitaire boards with peeking, to obtain an algorithm to solve Shisen-Sho boards. We sample several Shisen-Sho and Mahjong Solitaire layouts for solvability for Shisen-Sho and Mahjong Solitaire.
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Taxonomy
Topicsgraph theory and CDMA systems · Advanced Graph Theory Research · Constraint Satisfaction and Optimization