The minimum-distance constraint links a set of selected points to the smallest distance between any selected pair. A direct constraint-programming encoding is clear, but introduces a quadratic family of auxiliary distance variables and propagators.

This paper studies direct Gecode implementations ranging from pairwise propagators to global pair-support scans, advisor-backed support maintenance, and a conflict-matching upper bound. Preliminary experiments on p-dispersion instances show that direct propagation can avoid decomposition overhead, while also making clear that stronger propagation is not automatically faster. The simple pairwise forward-bound propagator remains a useful baseline; advisors and matching-based bounds are promising additions.