• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.24 no.3
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• pp.95-101
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• 2024

The numberlink puzzle(NLP), which non-crossings with other numbers of connection in connecting lines through empty cells between a given pair of numbers, is an NP-complete problem with no known way to solve the puzzle in polynomial time. Until now, arbitrary numbers have been selected and puzzles have been solved using trial-and-error methods. This paper converts empty cells into vertices in lattice graphs connected by edge between adjacent cells for a given problem. Next, a straight line was drawn between the pairs of numbers and divided into groups of numbers where crossing occurred. A bypass route was established to avoid intersection in the cross-number group. Applying the proposed algorithm to 18 benchmarking data showed that the puzzle could be solved with a linear time complexity of O(n) for all data.