Heuristics for Influence Maximization with Tiered Influence and Activation thresholds

TL;DR

This paper studies Minimum Influential Seeds (MINFS), a tiered diffusion variant of influence maximization that introduces a propagation range and node-specific influence and activation thresholds. It proposes three heuristics—Average Degree, Closest First, and Backbone-Based—plus a pruning technique, all designed to construct compact seed sets that influence all nodes within the propagation limit. Compared to existing MINFS methods, the proposed approaches, including BFS/DFS greedy variants with pruning, show improved seed-set quality across dense and sparse graphs and real-world datasets. The work provides practical guidance for seed selection under realistic diffusion constraints and suggests future exploration with metaheuristics such as genetic algorithms.

Abstract

The information flows among the people while they communicate through social media websites. Due to the dependency on digital media, a person shares important information or regular updates with friends and family. The set of persons on social media forms a social network. Influence Maximization (IM) is a known problem in social networks. In social networks, information flows from one person to another using an underlying diffusion model. There are two fundamental diffusion models: the Independent Cascade Model (ICM) and the Linear Threshold Model (LTM). In this paper, we study a variant of the IM problem called Minimum Influential Seeds (MINFS) problem proposed by Qiang et al.[16]. It generalizes the classical IM problem with LTM as the diffusion model. Compared to IM, this variant has additional parameters: the influence threshold for each node and the propagation range. The propagation range is a positive integer that specifies how far the information can propagate from a node. A node on the network is not immediately influenced until it receives the same information from enough number of neighbors (influence threshold). Similarly, any node does not forward information until it receives the same information from a sufficient number of neighbors (activation threshold). Once a node becomes activated, it tries to activate or influence its neighbors. The MINFS problem aims to select the minimum number of initial spreader nodes such that all nodes of the graph are influenced. In this paper, we extend the study of the MINFS problem. We propose heuristics that construct seed sets based on the average degree of non-activated nodes, closest first, and backbone-based heaviest path.

Figures (4)

• Figure 1: The spreader list of nodes(in light red color) is $\hat{S} = [5,1,4,9,8,10,6]$ and influenced vertices are in white (shown in the left). The PRUNING removes extra spreader node 5(in red) and returns $[1,4,9,8,10,6]$ because $5$ is activated by $4,8,9, 10$ (shown on the right).
• Figure 2: The first seed vertex is $2$ and the second most inactive vertex within two hops is $5$. We see here $2$ and $5$ are activating vertex $4$.
• Figure 3: When propagation range $p=3$, comparison of the results between the proposed algorithms and 2023tieredInf. Algorithm numbers 1 (DFS-GREEDY 2023tieredInf) and 2 (BFS-GREEDY 2023tieredInf) are proposed by 2023tieredInf, and we are proposing algorithm numbers 3 (DFS-GREEDY-PRUNNING ), 4 (BFS-GREEDY-PRUNNING ), 5(BACKBONE-BASED ), 6(AVERAGE-DEGREE ). The algorithm numbers are denoted on the X-axis of the bars, and the Y-axis denotes the size of the seed set.
• Figure 4: When propagation rang $p=diameter(G)$, the comparison of the results between the proposed algorithms and 2023tieredInf. Algorithm numbers 1 (DFS-GREEDY 2023tieredInf) and 2 (BFS-GREEDY 2023tieredInf) are proposed by 2023tieredInf, and we are proposing algorithm numbers 3 (DFS-GREEDY-PRUNNING ), 4 (BFS-GREEDY-PRUNNING ), 5(BACKBONE-BASED ), 6(AVERAGE-DEGREE ). The algorithm numbers are denoted on the X-axis of the bars, and the Y-axis denotes the size of the seed set.