NP-Hardness of Rotation Type Cell-Mazes

Shiro AOKI  Hiro ITO  Hideyuki UEHARA  Mitsuo YOKOYAMA  Tsuyoshi HORINOUCHI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E83-A   No.3   pp.492-496
Publication Date: 2000/03/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section LETTER (Special Section of Selected Papers from the 12th Workshop on Circuits and Systems in Karuizawa)
puzzle,  maze,  computational complexity,  NP-hard,  polynomial-time,  

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In this paper, a puzzle called Cell-Maze is analyzed. In this puzzle, cells are arranged in checker board squares. Each cell is rotated when a player arrives at the cell. Cell-Maze asks whether or not a player started from a start cell can reach a goal cell. The reachability problem for ordinary graphs can be easily solved in linear time, however a reachability problem for the network such as Cell-Maze may be extremely difficult. In this paper, NP-hardness of this puzzle is proved. It is proved by reducing Hamiltonian Circuit Problem of directed planar graph G such that each vertex involved in just three arcs. Furthermore, we consider subproblems, which can be solved in polynomial time.