Ordering strategy for applying certified joins

Determine an effective strategy for ordering the application of certified join operations when iteratively combining cut and join partial optimality conditions for cubic correlation clustering, including how the ordering impacts the fraction of variables that can be fixed and how to select heuristics to optimize this effect.

Background

The paper shows that cut and join conditions interact and that joins can change the instance, after which conditions are re-applied iteratively. The authors emphasize that the fraction of variables fixed depends on the order in which certified joins are applied.

They explicitly leave open which ordering strategy should be used, suggesting that heuristic design for ordering may significantly affect practical performance.