Online Myopic Network Covering

Abstract: Efficient marketing or awareness-raising campaigns seek to recruit $n$ influential individuals -- where $n$ is the campaign budget -- that are able to cover a large target audience through their social connections. So far most of the related literature on maximizing this network cover assumes that the social network topology is known. Even in such a case the optimal solution is NP-hard. In practice, however, the network topology is generally unknown and needs to be discovered on-the-fly. In this work we consider an unknown topology where recruited individuals disclose their social connections (a feature known as {\em one-hop lookahead}). The goal of this work is to provide an efficient greedy online algorithm that recruits individuals as to maximize the size of target audience covered by the campaign. We propose a new greedy online algorithm, Maximum Expected $d$-Excess Degree (MEED), and provide, to the best of our knowledge, the first detailed theoretical analysis of the cover size of a variety of well known network sampling algorithms on finite networks. Our proposed algorithm greedily maximizes the expected size of the cover. For a class of random power law networks we show that MEED simplifies into a straightforward procedure, which we denote MOD (Maximum Observed Degree). We substantiate our analytical results with extensive simulations and show that MOD significantly outperforms all analyzed myopic algorithms. We note that performance may be further improved if the node degree distribution is known or can be estimated online during the campaign.