{"ID":23475157,"CreatedAt":"2026-09-18T01:09:05.407443952Z","UpdatedAt":"2026-09-20T18:11:56.143995915Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.19960","arxiv_id":"2609.19960","title":"Exact Greedy Influence Maximization in Linear Time on Bounded-Treewidth Graphs","abstract":"Computing influence spread under the Independent Cascade (IC) model is #P-hard, and influence maximization is commonly approached using Monte Carlo or reverse-reachable-set sampling. We study IC diffusion on bounded-treewidth graphs. Using probability distributions over separator reachability relations, we obtain exact influence evaluation in $O(n2^{O(w^2)}\\operatorname{poly}(w))$ time for a graph with $n$ nodes and treewidth $w$. Our main contribution is an exact all-marginal-gains algorithm. We introduce variable artificial source edges and show that, at a deterministic seed set, the derivative with respect to each source-edge probability equals the corresponding greedy marginal gain. Reverse-mode differentiation therefore computes all marginal gains simultaneously with the same asymptotic complexity as one exact influence evaluation. This yields an exact implementation of classical greedy influence maximization in $O(Kn2^{O(w^2)}\\operatorname{poly}(w))$ time, linear in graph size for fixed $w$ and seed budget $K$. We also show that the separator-relation representation has tight $2^{Θ(w^2)}$ state complexity within exact context-independent compositional separator summaries. This contrasts with the NP-hardness of globally optimal IC influence maximization already on graphs of treewidth one and pathwidth two. Experiments on synthetic bounded-treewidth networks are consistent with linear scaling for fixed width and show that runtime is largely insensitive to propagation and seed-activation probabilities. In demanding diffusion regimes, the method substantially outperforms reverse-reachable-set and optimized Monte Carlo greedy baselines while computing greedy marginal gains exactly.","short_abstract":"Computing influence spread under the Independent Cascade (IC) model is #P-hard, and influence maximization is commonly approached using Monte Carlo or reverse-reachable-set sampling. We study IC diffusion on bounded-treewidth graphs. Using probability distributions over separator reachability relations, we obtain exact...","url_abs":"https://arxiv.org/abs/2609.19960","url_pdf":"https://arxiv.org/pdf/2609.19960v1","authors":"[\"Matic Požar\"]","published":"2026-09-17T09:30:49Z","proceeding":"cs.DS","tasks":"[\"cs.DS\"]","methods":"[\"Diffusion Model\"]","has_code":false}