General Rumor Blocking: An efficient random algorithm with martingale approach

Abstract

Rumor Blocking, an important optimization problem in social network, has been extensively studied in the literature. Given social network G=(V,E) and rumor seed set A, the goal is asking for k protector seeds that protect the largest expected number of social individuals by truth. However, the source of rumor is always uncertain, rather than being predicted or being known in advance in the real situations, while rumor spreads like wildfire on the Internet.This paper presents General Rumor Blocking with unpredicted rumor seed set (randomized A) and various personal profits while being protected (weights of nodes in V). We first show that the objective function of this problem is non-decreasing and submodular, and thus a (1−1/e) approximate solution can be returned by greedy approach. We then propose an efficient random algorithm R-GRB which returns a (1−1/e−ε) approximate solution with at least 1−n−ℓ probability. We show that it runs in O(m(n−r)(klog⁡(n−r)+ℓlog⁡n)/ε2) expected time, where m=|E|, n=|V|, r=|A| and k is the number of protector seeds. Finally, we conduct extensive experiments to evaluate the R-GRB and show that it is superior in both theory and experiment.