Clique constraints enter exact causal structure learning: no uniform speedup, and gains hinge on graph density and cut management
Exact causal structure learning solves for a globally optimal directed acyclic graph with mixed-integer programming, but its branch-and-cut search is costly. This work adds an upper bound on the maximum clique size of the learned undirected skeleton, using lazy cycle and clique constraints to reject locally over-dense subgraphs at integer candidates. On static linear-Gaussian synthetic graphs, clique constraints do not uniformly accelerate optimization; their benefit depends on graph density, sample size, and cut-management policy, while tighter valid Big-M bounds reduced the fixed-budget optimality gap in most tested settings.