Future superiority of PR over TSP for reordering overhead

Determine whether the conclusion that partition refinement (PR) reorderings require substantially less time and working storage than traveling salesman problem (TSP)–based reorderings—making PR the method of choice for reordering columns within supernodes—will continue to hold in the future across further developments and problem instances.

Background

The comparative paper finds that TSP and PR produce reorderings of similar quality for reducing RLB factorization times, but PR has dramatically lower overhead in both runtime and workspace to compute reorderings, leading the authors to conclude PR is the method of choice.

The authors formulate a forward-looking conjecture that this advantage of PR will persist, while noting the possibility of future improvements to either method.

References

We conjecture that this will remain the case in the future; it will be interesting to see if these two methods are subject to significant improvements in the future.

— A comparison of two effective methods for reordering columns within supernodes (2501.08395 - Karsavuran et al., 14 Jan 2025) in Section 5 (Conclusion)