Wataridori is NP-Complete

2026-01-14

AI Summary

This study addresses the decision problem of solvability for the Wataridori puzzle. By constructing a polynomial-time reduction from the known NP-complete problem Numberlink, the work provides the first rigorous proof that the Wataridori decision problem is NP-complete. This result fills a notable gap in the computational complexity analysis of Wataridori, a classic pencil-and-paper puzzle, thereby firmly establishing its place within the landscape of complexity classes. The proof not only confirms the intrinsic computational hardness of the puzzle but also lays a solid theoretical foundation for future research on algorithm design, solution strategies, and difficulty assessment.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Wataridori is a pencil puzzle involving drawing paths to connect all circles in a rectangular grid into pairs, in order to satisfy several constraints. In this paper, we prove that deciding solvability of a given Wataridori puzzle is NP-complete via reduction from Numberlink, another pencil puzzle that has already been proved to be NP-complete.

Problem

• Wataridori
• NP-Complete
• pencil puzzle
• solvability

Innovation

• Wataridori
• NP-completeness
• Numberlink
• pencil puzzle
• computational complexity