A Thorough Comparison Between Independent Cascade and Susceptible-Infected-Recovered Models

TL;DR

This work systematically compares the IC and SIR diffusion processes on networks, revealing that, when edge marginals are matched via $p_{u,v}$, IC yields at least as much influence as SIR and can do so by a large margin in some networks. The authors introduce a coupling via live-edge graphs and reverse reachable sets to prove IC's dominance and to show that seeds optimal for IC may differ from those optimal for SIR, motivating model-specific seeding strategies. They adapt the reverse-reachable-set based IMM framework to design $(1-1/e-\varepsilon)$-approximation algorithms for influence maximization under the SIR and TSIR models, achieving near-linear running times in practice and providing theoretical guarantees. Comprehensive experiments on real datasets corroborate the theoretical findings and demonstrate the practical viability and scalability of the proposed SIRIMM and TSIRIMM algorithms, while also highlighting the limitations of IC-based baselines when faced with SIR/TSIR dynamics.

Abstract

We study cascades in social networks with the independent cascade (IC) model and the Susceptible-Infected-recovered (SIR) model. The well-studied IC model fails to capture the feature of node recovery, and the SIR model is a variant of the IC model with the node recovery feature. In the SIR model, by computing the probability that a node successfully infects another before its recovery and viewing this probability as the corresponding IC parameter, the SIR model becomes an "out-going-edge-correlated" version of the IC model: the events of the infections along different out-going edges of a node become dependent in the SIR model, whereas these events are independent in the IC model. In this paper, we thoroughly compare the two models and examine the effect of this extra dependency in the SIR model. By a carefully designed coupling argument, we show that the seeds in the IC model have a stronger influence spread than their counterparts in the SIR model, and sometimes it can be significantly stronger. Specifically, we prove that, given the same network, the same seed sets, and the parameters of the two models being set based on the above-mentioned equivalence, the expected number of infected nodes at the end of the cascade for the IC model is weakly larger than that for the SIR model, and there are instances where this dominance is significant. We also study the influence maximization problem with the SIR model. We show that the above-mentioned difference in the two models yields different seed-selection strategies, which motivates the design of influence maximization algorithms specifically for the SIR model. We design efficient approximation algorithms with theoretical guarantees by adapting the reverse-reachable-set-based algorithms, commonly used for the IC model, to the SIR model. Finally, we conduct experimental studies over real-world datasets.

Figures (6)

• Figure 1: An instance to show the significant dominance. A vertex $v$ is connected to $b$ vertices by $b$ dashed edges, and these $b$ vertices are connected to a vertex $u$ by $b$ solid edges. Finally, $u$ is connected to $n_0$ vertices by $n_0$ solid edges. The solid edges are "deterministic", meaning that the parameters $\beta$ and $p$ in both $\textnormal{IC}\xspace$ and $\textnormal{SIR}\xspace$ models are set to $1$. For the dashed edges, they share the same $\textnormal{SIR}\xspace$ parameters $\beta$ and $\gamma$, and their $\textnormal{IC}\xspace$ parameter is decided based on $\beta$, $\gamma$ and \ref{['eqn:IC-SIR']}. The values of $b$, $n_0$, $\beta$, and $\gamma$ are to be decided.
• Figure 2: A graph to show the discrepancy of seeding strategy in $\textnormal{IC}\xspace$ and $\textnormal{SIR}\xspace$.
• Figure 3: The performances of the same $S$ under $\textnormal{IC}\xspace$ and $\textnormal{SIR}\xspace$, with a set of matching parameters $p$, $\beta$ and $\gamma$, respectively. Due to the significant overall fluctuations in the data, we use an inset plot to highlight the changes within a specific range. Without loss of generality, we show the specific fluctuation of Influence on the point when $p=0.1$.
• Figure 4: Comparing the influence spread of $\mathtt{SIRIMM}\xspace$ with baseline methods.
• Figure 5: Comparing the influence spread of $\mathtt{TSIRIMM}\xspace$ with baseline methods.

Theorems & Definitions (31)

• Definition 1: Diffusion Model and Influence Spread KKT15
• Definition 2: Influence Maximization KKT15
• Remark
• Definition 3: Live-edge Graph Formulation
• Example 1
• Proposition 3
• Proposition 4
• Example 2
• Proposition 5
• Definition 6: Reverse Reachable Set