Greedy Maximization Framework for Graph-based Influence Functions

TL;DR

This paper introduces a unified framework for influence maximization in graphs, providing a general class of influence functions and a meta-algorithm with strong approximation guarantees and efficient computation.

Contribution

It defines a broad class of influence functions extending previous models and proposes a meta-algorithm with near-linear runtime and strong approximation guarantees.

Findings

Unified influence function class beyond coverage functions

Meta-algorithm achieves near-linear computation

Strong approximation guarantees for influence maximization

Abstract

The study of graph-based submodular maximization problems was initiated in a seminal work of Kempe, Kleinberg, and Tardos (2003): An {\em influence} function of subsets of nodes is defined by the graph structure and the aim is to find subsets of seed nodes with (approximately) optimal tradeoff of size and influence. Applications include viral marketing, monitoring, and active learning of node labels. This powerful formulation was studied for (generalized) {\em coverage} functions, where the influence of a seed set on a node is the maximum utility of a seed item to the node, and for pairwise {\em utility} based on reachability, distances, or reverse ranks. We define a rich class of influence functions which unifies and extends previous work beyond coverage functions and specific utility functions. We present a meta-algorithm for approximate greedy maximization with strong approximation quality guarantees and worst-case near-linear computation for all functions in our class. Our meta-algorithm generalizes a recent design by Cohen et al (2014) that was specific for distance-based coverage functions.