### 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.

Original language | English (US) |
---|---|

Article number | 10 |

Journal | ACM Transactions on Computational Logic |

Volume | 14 |

Issue number | 2 |

DOIs | |

State | Published - Jun 2013 |

Externally published | Yes |

### Fingerprint

### Keywords

- Approximation algorithms
- Generalized annotated programs
- Social network

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science
- Computational Mathematics
- Logic

### Cite this

*ACM Transactions on Computational Logic*,

*14*(2), [10]. https://doi.org/10.1145/2480759.2480762

**Using generalized annotated programs to solve social network diffusion optimization problems.** / Shakarian, Paulo; Broecheler, Matthias; Subrahmanian, V. S.; Molinaro, Cristian.

Research output: Contribution to journal › Article

*ACM Transactions on Computational Logic*, vol. 14, no. 2, 10. https://doi.org/10.1145/2480759.2480762

}

TY - JOUR

T1 - Using generalized annotated programs to solve social network diffusion optimization problems

AU - Shakarian, Paulo

AU - Broecheler, Matthias

AU - Subrahmanian, V. S.

AU - Molinaro, Cristian

PY - 2013/6

Y1 - 2013/6

N2 - 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.

AB - 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.

KW - Approximation algorithms

KW - Generalized annotated programs

KW - Social network

UR - http://www.scopus.com/inward/record.url?scp=84881461006&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84881461006&partnerID=8YFLogxK

U2 - 10.1145/2480759.2480762

DO - 10.1145/2480759.2480762

M3 - Article

VL - 14

JO - ACM Transactions on Computational Logic

JF - ACM Transactions on Computational Logic

SN - 1529-3785

IS - 2

M1 - 10

ER -