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

Parth Nobel, Akshay Agrawal, Stephen Boyd

Abstract:

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 Simkin’s formulation, a sharper bound developed by Knuth,
and a Newton method that scales to large problem instances, to find even
sharper bounds.