Computing Tighter Bounds on the n-Queens Constant via Newton's Method

P. Nobel, A. Agrawal, S. Boyd

Manuscript, posted December 2021.

In recent work Simkin shows that bounds on an exponent occurring in the famous n-queens problem can be evaluated by solving convex optimization problems, allowing him to find bounds far tighter than previously known. In this note we use Simkinā€™s formulation, a sharper bound developed by Knuth, and a Newton method that scales to large problem instances, to find even sharper bounds.