Avoiding explicit separator-relation states in exact bounded-treewidth IC inference

Establish whether exact Independent Cascade influence inference on bounded-treewidth graphs can avoid explicit separator-relation states by using a fundamentally different, possibly more global, representation.

Background

The exact inference method represents distributions over reachability relations on separators. The paper proves that exact context-independent compositional summaries may require 2^{Omega(w^2)} distinguishable states in the worst case, although restricted graph families may permit smaller representations.

The stated open question concerns whether this lower bound for the specified summary framework can be bypassed altogether by an alternative representation that does not explicitly enumerate separator-relation states, potentially reducing the practical dependence on treewidth.