Satisfiability parsimoniously reduces to the Tantrix™ rotation puzzle problem

Authors:
Dorothea Baumeister;Jörg Rothe
Affiliations:
Institut für Informatik, Universität Düsseldorf, Düsseldorf, Germany;Institut für Informatik, Universität Düsseldorf, Düsseldorf, Germany
Venue:
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
Year:
2007

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Abstract

Holzer and Holzer [HH04] proved that the TantrixTM rotation puzzle problem is NP-complete. They also showed that for infinite rotation puzzles, this problem becomes undecidable.We study the counting version and the unique version of this problem. We prove that the satisfiability problem parsimoniously reduces to the TantrixTM rotation puzzle problem. In particular, this reduction preserves the uniqueness of the solution, which implies that the unique TantrixTM rotation puzzle problem is as hard as the unique satisfiability problem, and so is DPcomplete under polynomial-time randomized reductions, where DP is the second level of the boolean hierarchy over NP.