MTRC: multi-scale topology-guided residual coverage for finite-horizon SIR influence maximization

Influence maximization seeks a size-constrained seed set that maximizes diffusion under a specified propagation process. In finite-horizon susceptible–infected–recovered (SIR) diffusion, a candidate’s value depends on recovery-limited transmission paths and on propagation opportunities not already represented by earlier seeds. Static rankings do not directly optimize this set-dependent objective, while simulation-based greedy selection is costly and canonical reverse-sampling methods are commonly formulated for independent-cascade live-edge processes. This paper proposes multi-scale topology-guided residual coverage (MTRC). Node activity, k -shell support, and neighbor-degree heterogeneity are organized into a node–scale–channel tensor and contracted into a multi-scale topology potential. Reverse-diffusion samples are then generated from finite-horizon SIR realizations that encode first-success transmission delays, infectious durations, recovery, and the propagation horizon. Seeds are selected by residual sample coverage; the topology prior refines only candidates whose sampled marginal gain preserves a prescribed fraction of the current maximum. For a fixed sample bank, the coverage objective is monotone and submodular, and the selection rule yields a 1 − e −(1− δ ) lower bound for that finite-sample objective. Experiments on twelve networks compare MTRC with greedy, reverse-sampling, community-aware, redundancy-aware, and structural baselines. MTRC attains an average AUC rank of 2.17 and improves normalized spread AUC over the strongest non-CELF++ baseline by 3.46% on average. On the eight networks evaluated with CELF++, MTRC is 2.10% lower on average but requires substantially less selection time. Ablation and redundancy analyses identify residual coverage as the main source of improvement, with structural refinement providing a smaller dispersion benefit.