From Competition to Complementarity: Comparative Influence Diffusion and Maximization (1507.00317v3)

Abstract: Influence maximization is a well-studied problem that asks for a small set of influential users from a social network, such that by targeting them as early adopters, the expected total adoption through influence cascades over the network is maximized. However, almost all prior work focuses on cascades of a single propagating entity or purely-competitive entities. In this work, we propose the Comparative Independent Cascade (Com-IC) model that covers the full spectrum of entity interactions from competition to complementarity. In Com-IC, users' adoption decisions depend not only on edge-level information propagation, but also on a node-level automaton whose behavior is governed by a set of model parameters, enabling our model to capture not only competition, but also complementarity, to any possible degree. We study two natural optimization problems, Self Influence Maximization and Complementary Influence Maximization, in a novel setting with complementary entities. Both problems are NP-hard, and we devise efficient and effective approximation algorithms via non-trivial techniques based on reverse-reachable sets and a novel "sandwich approximation". The applicability of both techniques extends beyond our model and problems. Our experiments show that the proposed algorithms consistently outperform intuitive baselines in four real-world social networks, often by a significant margin. In addition, we learn model parameters from real user action logs.

• The paper introduces the Com-IC model to simulate both competitive and complementary entity interactions in social networks.
• It leverages an automaton-based decision process with GAP parameters to enhance traditional diffusion models.
• Efficient approximation algorithms using reverse-reachable sets and a sandwich technique outperform baseline methods in real-world tests.

Comparative Influence Diffusion and Maximization: Analysis and Algorithmic Innovations

The paper "From Competition to Complementarity: Comparative Influence Diffusion and Maximization" addresses the classic problem of influence maximization in social networks and proposes a new model called Comparative Independent Cascade (Com-IC). This model is designed to capture the full range of interactions between competing entities, from pure competition to complementarity, facilitating a more nuanced analysis of influence diffusion processes.

Introduction and Background

The influence maximization problem traditionally focuses on identifying a small set of influential users in a social network to maximize the spread of a propagating entity, such as a product or an idea. Prior studies have largely concentrated on two types of models: single-entity models like the Independent Cascade (IC) and Linear Threshold (LT) models and competitive models where entities compete for adoption. However, these models fall short in contexts where entities can be complementary rather than purely competitive.

Com-IC Model: A Novel Framework

The Com-IC model extends the classical IC model by introducing an automaton-based decision process at the node level. It consists of two components:

1. Edge-Level Propagation: Similar to conventional models, this governs the way information about an entity propagates through the network.
2. Node-Level Automaton (NLA): This novel component determines actual adoption decisions based on Global Adoption Probabilities (GAPs), allowing for the simulation of varying degrees of competition and complementarity between entities.

Key to the Com-IC model is the introduction of GAPs, parameters that encode the likelihood of adoption of one entity given the adoption of another, thus offering a flexible framework to model intricate relationships like substitution (competition) and complementary goods.

Optimization Problems

The paper introduces two optimization problems within the framework of complementary entities:

• Self Influence Maximization (SelfInfMax): Given a set of seeds for one entity, identify seeds for another to maximize the influence spread of the former.
• Complementary Influence Maximization (CompInfMax): Given a set of seeds for one entity, find seeds for the other to maximize the complementary influence.

Both problems are NP-hard, and the authors provide efficient approximation algorithms. The use of reverse-reachable (RR) sets and a novel "sandwich approximation" technique forms the core of their solution approach, allowing for effective approximations even when classical submodularity does not hold.

Empirical Results and Theoretical Implications

Experiments conducted on real-world networks demonstrate that the proposed Com-IC algorithms consistently outperform baseline methods. The superiority is evident in handling cases with learned GAPs from datasets like Flixster and Douban, where the model's flexibility is crucial to capturing real-world item interactions.

Theoretically, the work pushes the boundaries of current understanding by accommodating complex social interactions beyond pure competition, paving the way for more realistic modeling and analysis of social influence processes.

Conclusion and Future Work

This research significantly advances the paper of influence maximization by integrating the concepts of competition and complementarity within a unified framework. It offers new algorithmic techniques that could be impactful for future studies exploring multi-entity interactions in networks. Future work could extend this model to scenarios with multiple complementary and competing items, shedding further light on the nuances of social dynamics.

In sum, the Com-IC model represents a substantial methodological and algorithmic development with both practical significance for viral marketing strategies and theoretical implications for influence diffusion modeling.