Kissing Number Decision Problem

Determine the computational complexity of the Kissing Number decision problem for compact semialgebraic sets, i.e., decide whether there exist k non-overlapping congruent copies each touching the given set.

Background

The kissing number problem asks for the maximum number of congruent shapes touching a given shape without overlap.

The survey points out that while solver-based approaches can handle instances with explicit bounds, the overall complexity classification remains open.