发表机构
University of Primorska（普里莫斯卡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对有界树宽图上的IC模型影响力最大化，提出精确全边际增益算法，利用反向模式微分在近线性时间内实现经典贪心算法，并证明其状态复杂度紧致，实验验证了高效性。
AI 中文摘要
在独立级联（IC）模型下计算影响力传播是#P难的，影响力最大化通常采用蒙特卡洛或反向可达集采样方法。我们研究有界树宽图上的IC扩散。利用分隔符可达性关系上的概率分布，我们对于具有$n$个节点和树宽$w$的图，实现了$O(n2^{O(w^2)}\operatorname{poly}(w))$时间的精确影响力评估。我们的主要贡献是一个精确的全边际增益算法。我们引入可变人工源边，并证明在确定性种子集下，每个源边概率的导数等于相应的贪心边际增益。因此，反向模式微分可以同时计算所有边际增益，其渐近复杂度与一次精确影响力评估相同。这产生了经典贪心影响力最大化的精确实现，时间复杂度为$O(Kn2^{O(w^2)}\operatorname{poly}(w))$，对于固定的$w$和种子预算$K$，在图大小上是线性的。我们还证明了在精确的上下文无关组合分隔符摘要中，分隔符关系表示具有紧的$2^{\Theta(w^2)}$状态复杂度。这与全局最优IC影响力最大化即使在树宽为一、路径宽为二的图上也是NP难的形成了对比。在合成有界树宽网络上的实验与固定宽度下的线性扩展一致，并表明运行时间在很大程度上对传播概率和种子激活概率不敏感。在高要求扩散场景中，该方法在精确计算贪心边际增益的同时，显著优于反向可达集和优化的蒙特卡洛贪心基线。
英文摘要
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.
Comments22 pages, 2 figures, 2 tables
