The connection between users in social networks can be maintained for a certain period of time, and the static network structure formed provides the basic conditions for various kinds of research, especially for discovering customer groups that can generate great influence, which is important for product promotion, epidemic prevention and control, and public opinion supervision, etc. However, the computational process of influence maximization ignores the timeliness of interaction behaviors among users, the screened target users cannot diffuse information well, and the time complexity of relying on greedy rules to handle the influence maximization problem is high. Therefore, this paper analyzes the influence of the interaction between nodes in dynamic social networks on information dissemination, extends the classical independent cascade model to a dynamic social network dissemination model based on effective links, and proposes a two-stage influence maximization solution algorithm (Outdegree Effective Link—OEL) based on node degree and effective links to enhance the efficiency of problem solving. In order to verify the effectiveness of the algorithm, five typical influence maximization methods are compared and analyzed on four real data sets. The results show that the OEL algorithm has good performance in propagation range and running time.

The influence maximization problem is designed to seek a set of nodes in a social network so that the set has the maximum information propagation capacity on the network. In response to the inefficiency of existing greedy algorithms and the low accuracy of centrality-based heuristics, we propose an improved differential evolution algorithm (IDDE) based on the network discretization in this paper. The algorithm improves the variance rule of the differential evolution algorithm, takes the discrete number and discrete granularity of the remaining network after the removal of the target node as the index to evaluate the importance of the node, and proposes a fitness function based on the robustness of the network. The method embodies symmetry in two aspects. Firstly, the global connectivity among nodes in the network decreases as the number of target nodes removed in the social network increases. Secondly, the gain of global influence range gradually becomes smaller as the number of target nodes screened by the proposed method increases. We conducted comparison experiments on four real datasets of different sizes, and the results show that the IDDE algorithm outperforms the comparison algorithm.

Influence maximization seeks a limited seed set that maximizes diffusion spread. Topology-based rankings are efficient but often ignore finite-horizon dynamics and seed-set redundancy, whereas simulation-assisted greedy methods can be computationally expensive. To balance effectiveness, efficiency, and interpretability, this paper proposes temporal multi-path marginal coverage (TMPMC), a deterministic surrogate for finite-horizon susceptible–infected–recovered (SIR) influence maximization. TMPMC estimates source–target probabilities through temporal path propagation, global noisy-OR aggregation over retained paths, and target-level marginal coverage. Unlike IC- or LT-oriented path approximations, TMPMC accounts for repeated infection attempts, recovery risk, feasible arrival times, and a finite propagation horizon. Its monotonicity and submodularity results apply to the surrogate objective, not to the exact stochastic SIR expectation. Across 1,000 common-random-number SIR possible worlds, TMPMC obtains a higher paired AUC than the strongest ranking or heuristic reference on all twelve networks, with an average relative gain of 6.39%. Comparisons with the same-model CELF++ reference, finite-depth IC-based cross-model RR references, and adapted learning-based references reveal a network-dependent effectiveness–efficiency trade-off rather than uniform dominance. High-precision diagnostics show strong within-budget and within-base candidate ranking fidelity, while diffusion-parameter, propagation-horizon, and unified single-thread time–memory analyses characterize robustness and computational scaling. These results support TMPMC as a training-free and interpretable surrogate when finite-horizon SIR-aware seed ranking is required.

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.

In pedagogy, the “Root of problem” is often used to express the core elements and basic theories of knowledge. In this paper, we design a teaching model based on root problem thinking under the guidance of OBE concept. The model leads students to condense the root problem by creating problematic scenarios and guiding them in the process of outcome-oriented heuristic teaching. Through the extension and expansion of core knowledge, the process of deepening knowledge from point to surface is realized. The teaching model can help students form excellent qualities of thinking in the process of analysis and synthesis, abstraction and generalization, systematization and concretization of thinking training. In order to further prove the effect of the new teaching mode, we implemented the teaching reform work for the teaching process of the Python Programming course of the Internet of Things Engineering major in the College of Computer Science, and achieved good teaching results.