On the Upper Bounds of Spread for Greedy Algorithms in Social Network Influence Maximization

Abstract

Influence maximization, defined as finding a small subset of nodes that maximizes spread of influence in social networks, is NP-hard under both Independent Cascade (IC) and Linear Threshold (LT) models, where many greedy-based algorithms have been proposed with the best approximation guarantee. However, existing greedy-based algorithms are inefficient on large networks, as it demands heavy Monte-Carlo simulations of the spread functions for each node at the initial step [7] . In this paper, we establish new upper bounds to significantly reduce the number of Monte-Carlo simulations in greedy-based algorithms, especially at the initial step. We theoretically prove that the bound is tight and convergent when the summation of weights towards (or from) each node is less than 1. Based on the bound, we propose a new Upper Bound based Lazy Forward algorithm ( UBLF in short) for discovering the top-k influential nodes in social networks. We test and compare UBLF with prior greedy algorithms, especially CELF [30] . Experimental results show that UBLF reduces more than 95 percent Monte-Carlo simulations of CELF and achieves about $2\hbox{-}10$ times speedup when the seed set is small.