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Composing the Queen’s Exile — A Knighted Chain Solution to the N-Queens Problem

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Abstract

The N-queens problem plays an important role in academic research and has many practical applications ranging from physics to biology and cryptography to protein folding. The complexity increases with increasing values of n. Solving for the location of queens arranged as knighted chains can reduce the time complexity and resource requirements, providing at least one fundamental solution for all n (n ≥ 4). An exhaustive memoir on the development of a heuristic algorithm to propose a plausible solution for the N-queens problem is presented. Every n is mapped into an instance of its even analogue, assigned to groups, and a solution is designed with knighted chain patterns. In case of odd n, the solution is extended to complete the composition. Furthermore, a generalised solution for all n (n ≥ 4) is presented. Composing the queen’s exile by knighted chains results in a symmetric solution that could both be solvable and verifiable.

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Authors and Affiliations

  1. Vivekanand Education Society’s Institute of Technology, Mumbai, India

    Abhinav Swaminathan

  2. Sardar Patel Institute of Technology, Mumbai, India

    Abhishek Swaminathan

  3. National Institute of Industrial Engineering, Maharashtra State, Mumbai, 400087, India

    Janardan Vaidyanathan

Authors
  1. Abhinav Swaminathan
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  2. Abhishek Swaminathan
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  3. Janardan Vaidyanathan
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AS, conceptualization, methodology, validation, visualization, and writing — review and editing. AS, conceptualization, methodology, visualization, supervision, and writing — review and editing. JV, conceptualization, methodology, resources, visualization, and writing — original draft.

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Correspondence to Janardan Vaidyanathan.

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Swaminathan, A., Swaminathan, A. & Vaidyanathan, J. Composing the Queen’s Exile — A Knighted Chain Solution to the N-Queens Problem. Oper. Res. Forum 5, 3 (2024). https://doi.org/10.1007/s43069-023-00284-7

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