Uniform random sampling of feasible TTP(3) solutions

Construct an algorithm that uniformly samples feasible solutions to the Traveling Tournament Problem with maximum trip length three, TTP(3), at random.

Background

Population-based algorithms for the TTP remain relatively underexplored, partly because generating many diverse feasible starting timetables is difficult. The paper emphasizes that a uniformly distributed sampler could support population-based methods and reduce reliance on canonical constructions. Whether such a sampler exists is explicitly posed as an open problem.

References

This brings us to the following open problem.

\begin{open} \label{open:initial} Does there exist an algorithm for uniformly sampling feasible solutions to TTP(3) at random? \end{open}

— The Traveling Tournament Problem: An Overview  (2609.03612 - Bulck et al., 3 Sep 2026) in Section 6, subsection “Heuristic Methods”