Targeted Influence Maximization In Labeled Social Networks with Non-Target Constraints

The objective of influence maximization problem is to find a set of highly influential nodes that maximizes the spread of influence in a social network. Such a set of nodes is called seed set. Targeted labeled influence maximization problem is an extension that attempts to find a seed set that maximizes influence among certain labeled nodes. However, in certain application areas such as market and political sciences, it is desirable to limit the spread of influence on certain set of nodes while maximizing the influence spread among different set of nodes. Motivated by this, in this work we formulate and study Constrained Targeted Influence Maximization problem where a network has two types of nodes --targets and non-targets. For a given k and theta, the objective is to find a k size seed set which maximizes the influence over the targets and keeps the influence over the non-targets within the threshold theta. We propose two algorithms based on the greedy approach and establish certain approximation guarantees. We extend this greedy algorithm to a Multi-Greedy algorithm. However, the pure greedy methods are not practically viable due to prohibitively high time overhead. To address that, we develop two-phase framework that will enable us to use multiple heuristic choices as subroutines. We experimentally show that several of these heuristic algorithms produce solutions whose quality is close to the quality of solutions produced by the greedy algorithm. We have developed a prototype framework and evaluated all the algorithms using social networks with different types and sizes

Effects of Time Horizons on Influence Maximization in the Voter Dynamics

In this paper we analyze influence maximization in the voter model with an active strategic and a passive influencing party in non-stationary settings. We thus explore the dependence of optimal influence allocation on the time horizons of the strategic influencer. We find that on undirected heterogeneous networks, for short time horizons, influence is maximized when targeting low-degree nodes, while for long time horizons influence maximization is achieved when controlling hub nodes. Furthermore, we show that for short and intermediate time scales influence maximization can exploit knowledge of (transient) opinion configurations. More in detail, we find two rules. First, nodes with states differing from the strategic influencer's goal should be targeted. Second, if only few nodes are initially aligned with the strategic influencer, nodes subject to opposing influence should be avoided, but when many nodes are aligned, an optimal influencer should shadow opposing influence.Comment: 22 page

Maximizing Activity in Ising Networks via the TAP Approximation

A wide array of complex biological, social, and physical systems have recently been shown to be quantitatively described by Ising models, which lie at the intersection of statistical physics and machine learning. Here, we study the fundamental question of how to optimize the state of a networked Ising system given a budget of external influence. In the continuous setting where one can tune the influence applied to each node, we propose a series of approximate gradient ascent algorithms based on the Plefka expansion, which generalizes the na\"{i}ve mean field and TAP approximations. In the discrete setting where one chooses a small set of influential nodes, the problem is equivalent to the famous influence maximization problem in social networks with an additional stochastic noise term. In this case, we provide sufficient conditions for when the objective is submodular, allowing a greedy algorithm to achieve an approximation ratio of $1-1/e$. Additionally, we compare the Ising-based algorithms with traditional influence maximization algorithms, demonstrating the practical importance of accurately modeling stochastic fluctuations in the system