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The n-Queens Problem in Higher Dimensions

2023

Thesis, Integer Programming,
Graph Theory,
Chess, Technical University Berlin

How many mutually non-attacking queens can be placed on a d-dimensional chessboard of size n? We provide a comprehensive overview on theoretical results, bounds, solution methods and the interconnectivity of the problem within topics of discrete optimization and combinatorics.

We present an integer programming formulation and several strengthenings, achieving a speedup in runtime between 15-70x over all instances.

MSc Thesis at Technical University Berlin, Institute of Mathematics, Discrete und Algorithmic Mathematics, supervised by Prof. Dr. Thorsten Koch