Combining Traditional Marketing and Viral Marketing with Amphibious Influence Maximization

In this paper, we propose the amphibious influence maximization (AIM) model that combines traditional marketing via content providers and viral marketing to consumers in social networks in a single framework. In AIM, a set of content providers and consumers form a bipartite network while consumers also form their social network, and influence propagates from the content providers to consumers and among consumers in the social network following the independent cascade model. An advertiser needs to select a subset of seed content providers and a subset of seed consumers, such that the influence from the seed providers passing through the seed consumers could reach a large number of consumers in the social network in expectation. We prove that the AIM problem is NP-hard to approximate to within any constant factor via a reduction from Feige's k-prover proof system for 3-SAT5. We also give evidence that even when the social network graph is trivial (i.e. has no edges), a polynomial time constant factor approximation for AIM is unlikely. However, when we assume that the weighted bi-adjacency matrix that describes the influence of content providers on consumers is of constant rank, a common assumption often used in recommender systems, we provide a polynomial-time algorithm that achieves approximation ratio of $(1-1/e-\epsilon)^3$ for any (polynomially small) $\epsilon > 0$. Our algorithmic results still hold for a more general model where cascades in social network follow a general monotone and submodular function.Comment: An extended abstract appeared in the Proceedings of the 16th ACM Conference on Economics and Computation (EC), 201

Maximizing Welfare in Social Networks under a Utility Driven Influence Diffusion Model

Motivated by applications such as viral marketing, the problem of influence maximization (IM) has been extensively studied in the literature. The goal is to select a small number of users to adopt an item such that it results in a large cascade of adoptions by others. Existing works have three key limitations. (1) They do not account for economic considerations of a user in buying/adopting items. (2) Most studies on multiple items focus on competition, with complementary items receiving limited attention. (3) For the network owner, maximizing social welfare is important to ensure customer loyalty, which is not addressed in prior work in the IM literature. In this paper, we address all three limitations and propose a novel model called UIC that combines utility-driven item adoption with influence propagation over networks. Focusing on the mutually complementary setting, we formulate the problem of social welfare maximization in this novel setting. We show that while the objective function is neither submodular nor supermodular, surprisingly a simple greedy allocation algorithm achieves a factor of $(1-1/e-\epsilon)$ of the optimum expected social welfare. We develop \textsf{bundleGRD}, a scalable version of this approximation algorithm, and demonstrate, with comprehensive experiments on real and synthetic datasets, that it significantly outperforms all baselines.Comment: 33 page

Locally Adaptive Optimization: Adaptive Seeding for Monotone Submodular Functions

The Adaptive Seeding problem is an algorithmic challenge motivated by influence maximization in social networks: One seeks to select among certain accessible nodes in a network, and then select, adaptively, among neighbors of those nodes as they become accessible in order to maximize a global objective function. More generally, adaptive seeding is a stochastic optimization framework where the choices in the first stage affect the realizations in the second stage, over which we aim to optimize. Our main result is a $(1-1/e)^2$-approximation for the adaptive seeding problem for any monotone submodular function. While adaptive policies are often approximated via non-adaptive policies, our algorithm is based on a novel method we call \emph{locally-adaptive} policies. These policies combine a non-adaptive global structure, with local adaptive optimizations. This method enables the $(1-1/e)^2$-approximation for general monotone submodular functions and circumvents some of the impossibilities associated with non-adaptive policies. We also introduce a fundamental problem in submodular optimization that may be of independent interest: given a ground set of elements where every element appears with some small probability, find a set of expected size at most $k$ that has the highest expected value over the realization of the elements. We show a surprising result: there are classes of monotone submodular functions (including coverage) that can be approximated almost optimally as the probability vanishes. For general monotone submodular functions we show via a reduction from \textsc{Planted-Clique} that approximations for this problem are not likely to be obtainable. This optimization problem is an important tool for adaptive seeding via non-adaptive policies, and its hardness motivates the introduction of \emph{locally-adaptive} policies we use in the main result

Influence maximization towards target users on social networks for information diffusion

Influence maximisation has been an area of active research in recent years. This study aims to extend the fundamental influence maximisation problem (IMP) with respect to a set of target users on a social network. It is important to aim at the target users to speed up the rate of information diffusion and reduce the information diffusion cost. In doing so, the MITU algorithm was formulated and compared with state of the art algorithms. Publicly available datasets were used in validating the proposed algorithm. It was found that the MITU identified all target nodes while significantly lowering the information diffusion cost function (IDCF) by up to 79%. The influence overlap problem was equally identified in the heuristic algorithm where the seed set size was reduced by an average of six times. Furthermore, the random influencer selection identifies target nodes better than the betweenness and PageRank centralities. The findings could help organisations to reach target users on social media in the shortest cycle

Influence maximisation towards target users on social networks for information diffusion

Influence maximisation has been an area of active research in recent years.This study aims to extend the fundamental influence maximisation problem (IMP) with respect to a set of target users on a social network.It is important to aim at the target users to speed up the rate of information diffusion and reduce the information diffusion cost.In doing so, the MITU algorithm was formulated and compared with state of the art algorithms.Publicly available datasets were used in validating the proposed algorithm.It was found that the MITU identified all target nodes while significantly lowering the information diffusion cost function (IDCF) by up to 79%.The influence overlap problem was equally identified in the heuristic algorithm where the seed set size was reduced by an average of six times.Furthermore, the random influencer selection identifies target nodes better than the betweenness and PageRank centralities.The findings could help organisations to reach target users on social media in the shortest cycle

Influence Maximization Towards Target Users on Social Networks for Information Diffusion

Influence maximisation has been an area of active research in recent years. This study aims to extend the fundamental influence maximisation problem (IMP) with respect to a set of target users on a social network. It is important to aim at the target users to speed up the rate of information diffusion and reduce the information diffusion cost. In doing so, the MITU algorithm was formulated and compared with state of the art algorithms. Publicly available datasets were used in validating the proposed algorithm. It was found that the MITU identified all target nodes while significantly lowering the information diffusion cost function (IDCF) by up to 79%. The influence overlap problem was equally identified in the heuristic algorithm where the seed set size was reduced by an average of six times. Furthermore, the random influencer selection identifies target nodes better than the betweenness and PageRank centralities. The findings could help organisations to reach target users on social media in the shortest cycle

Influence maximisation towards target users and minimal diffusion of information based on information needs

Influence maximisation within social network is essential to the modern business. Influence Maximisation Problem (IMP) involves the minimal selection of influencers that leads to maximum contagion while minimizing Diffusion Cost (DC). Previous models of IMP do not consider DC in spreading information towards target users. Furthermore, influencer selection for varying information needs was not considered which leads to influence overlaps and elimination of weak nodes. This study proposes the Information Diffusion towards Target Users (IDTU) algorithm to enhance influencer selection while minimizing the DC. IDTU was developed on greedy approach by using graph sketches to improve the selection of influencers that maximize influence spread to a set of target users. Moreover, the influencer identification based on specific needs was implemented using a General Additive Model on four fundamental centralities. Experimental method was used by employing five social network datasets including Epinions, Wiki-Vote, SlashDot, Facebook and Twitter from Stanford data repository. Evaluation on IDTU was performed against 3 greedy and 6 heuristics benchmark algorithms. IDTU identified all the specified target nodes while lowering the DC by up to 79%. In addition, the influence overlap problem was reduced by lowering up to an average of six times of the seed set size. Results showed that selecting the top influencers using a combination of metrics is effective in minimizing DC and maximizing contagion up to 77% and 32% respectively. The proposed IDTU has been able to maximize information diffusion while minimizing DC. It demonstrates a more balanced and nuanced approach regarding influencer selection. This will be useful for business and social media marketers in leveraging their promotional activities