Using Generalized Annotated Programs to Solve Social Network Diffusion Optimization Problems

Abstract

There has been extensive work in many different fields on how phenomena of interest (e.g., diseases, innovation, product adoption) "diffuse" through a social network. As social networks increasingly become a fabric of society, there is a need to make "optimal" decisions with respect to an observed model of diffusion. For example, in epidemiology, officials want to find a set of k individuals in a social network which, if treated, would minimize spread of a disease. In marketing, campaign managers try to identify a set of k customers that, if given a free sample, would generate maximal "buzz" about the product. In this article, we first show that the well-known Generalized Annotated Program (GAP) paradigm can be used to express many existing diffusion models. We then define a class of problems called Social Network Diffusion Optimization Problems (SNDOPs). SNDOPs have four parts: (i) a diffusion model expressed as a GAP, (ii) an objective function we want to optimize with respect to a given diffusion model, (iii) an integer k > 0 describing resources (e.g., medication) that can be placed at nodes, (iv) a logical condition VC that governs which nodes can have a resource (e.g., only children above the age of 5 can be treated with a given medication). We study the computational complexity of SNDOPs and show both NP-completeness results as well as results on complexity of approximation. We then develop an exact and a heuristic algorithm to solve a large class of SNDOPproblems and show that our GREEDY-SNDOP algorithm achieves the best possible approximation ratio that a polynomial algorithm can achieve (unless P = NP). We conclude with a prototype experimental implementation to solve SNDOPs that looks at a real-world Wikipedia dataset consisting of over 103,000 edges. ACM Reference Format:Shakarian, P., Broecheler, M., Subrahmanian, V. S. and Molinaro, C. 2013. Using generalized annotated programs to solve social network diffusion optimization problems.

ChoiceGAPs: Competitive Diffusion as a Massive Multi-player Game in Social Networks

“…It is important to note that [Kempe et al 2003] is a generalization of many important models in economics and social science such as [Granovetter 1978; Jackson and Yariv 2005; J. Goldenberg 2001] -which can be represented with our logic-programming based framework as we showed in [Shakarian et al 2013]. [Kempe et al 2003] is extended to a competive scenario in [Carnes et al 2007].…”

“…In this paper, we present the ChoiceGAP framework using which we can model competing diffusive processes via a mix of generalized annotated programs (GAPs) due to Kifer and Subrahmanian [Kifer and Subrahmanian 1992] and Choice Logic Programs proposed by Saccà and Zaniolo [Saccà and Zaniolo 1990]. The use of GAPs to model diffusion processes was already proposed in [Shakarian et al 2013;Broecheler et al 2010] -there, the authors show how many well-known diffusion models can be expressed as GAPs. 1 [Shakarian et al 2013] assumes only one diffusive process is occurring at a time and that there is no competition going on.…”

“…Even though we show that computing range answers to estimation queries exactly is intractable, we are able to identify classes of estimation queries that can be answered in polynomial time. We report on experiments we conducted with a real-world FaceBook data set surrounding the 2013 Italian election showing that our algorithms have good predictive accuracy with an Area Under a ROC Curve that, on average, is over 0.76.1 Specifically, the authors of [Shakarian et al 2013] show that they can express cascade models such as [Cha et al 2009a] used to model the spread of "favorites" in Flickr, tipping models such as the Jackson-Yariv model of product adoption in economics [Jackson and Yariv 2005], the SIR and the SIS models of disease spread [Anderson and May 1979;Hethcote 1976], as well as homophilic models such as those involving mobile phone usage [Aral et al 2009]. Thus, GAPs can be used to represent many different diffusion models and hence we do not repeat these representations here.…”

“…1 Specifically, the authors of [Shakarian et al 2013] show that they can express cascade models such as [Cha et al 2009a] used to model the spread of "favorites" in Flickr, tipping models such as the Jackson-Yariv model of product adoption in economics [Jackson and Yariv 2005], the SIR and the SIS models of disease spread [Anderson and May 1979;Hethcote 1976], as well as homophilic models such as those involving mobile phone usage [Aral et al 2009]. Thus, GAPs can be used to represent many different diffusion models and hence we do not repeat these representations here.…”

Fast influence-based coarsening for large networks

“…These dynamic processes are all closely related to virus propagation. General algorithms for information diffusion based optimization include [36]. Table 1 gives some of the notation.…”