Polynomial-time globally optimal LT influence maximization on bounded-width graphs

Determine whether globally optimal Linear Threshold influence maximization admits polynomial-time algorithms on graphs of bounded treewidth or bounded pathwidth.

Background

The paper develops exact inference and exact greedy optimization for the Independent Cascade model on bounded-treewidth graphs, while noting that globally optimal influence maximization remains NP-hard for IC even on trees and graphs of pathwidth at most two. In contrast, influence maximization under the Linear Threshold model is tractable on in-arborescences.

The paper observes that the Linear Threshold model has a triggering-set representation, but its incoming triggering edges are locally correlated rather than independent. This creates both an inference challenge and a complexity question: whether the tractability seen on in-arborescences extends to globally optimal Linear Threshold influence maximization on graphs with bounded treewidth or bounded pathwidth remains unresolved.