### Abstract

Diffusion on complex networks is often modeled as a stochastic process. Yet, recent work on strategic diffusion emphasizes the decision power of agents [1] and treats diffusion as a strategic problem. Here we study the computational aspects of strategic diffusion, i.e., finding the optimal sequence of nodes to activate a network in the minimum time. We prove that finding an optimal solution to this problem is NP-complete in a general case. To overcome this computational difficulty, we present an algorithm to compute an optimal solution based on a dynamic programming technique. We also show that the problem is fixed parameter-tractable when parametrized by the product of the treewidth and maximum degree. We analyze the possibility of developing an efficient approximation algorithm and show that two heuristic algorithms proposed so far cannot have better than a logarithmic approximation guarantee. Finally, we prove that the problem does not admit better than a logarithmic approximation, unless P=NP.

Original language | English |
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Journal | Theoretical Computer Science |

DOIs | |

Publication status | E-pub ahead of print - 30 Jan 2020 |

### Fingerprint

### Keywords

- Complex networks
- Influence maximization
- Network contagion
- Strategic diffusion

### Cite this

*Theoretical Computer Science*. https://doi.org/10.1016/j.tcs.2020.01.027

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*Theoretical Computer Science*. https://doi.org/10.1016/j.tcs.2020.01.027

**Computational aspects of optimal strategic network diffusion.** / Waniek, Marcin; Elbassioni, Khaled; Pinheiro, Flávio L.; Hidalgo, César A.; Alshamsi, Aamena.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Computational aspects of optimal strategic network diffusion

AU - Waniek, Marcin

AU - Elbassioni, Khaled

AU - Pinheiro, Flávio L.

AU - Hidalgo, César A.

AU - Alshamsi, Aamena

N1 - Waniek, M., Elbassioni, K., Pinheiro, F. L., Hidalgo, C. A., & Alshamsi, A. (2020). Computational aspects of optimal strategic network diffusion. Theoretical Computer Science. https://doi.org/10.1016/j.tcs.2020.01.027

PY - 2020/1/30

Y1 - 2020/1/30

N2 - Diffusion on complex networks is often modeled as a stochastic process. Yet, recent work on strategic diffusion emphasizes the decision power of agents [1] and treats diffusion as a strategic problem. Here we study the computational aspects of strategic diffusion, i.e., finding the optimal sequence of nodes to activate a network in the minimum time. We prove that finding an optimal solution to this problem is NP-complete in a general case. To overcome this computational difficulty, we present an algorithm to compute an optimal solution based on a dynamic programming technique. We also show that the problem is fixed parameter-tractable when parametrized by the product of the treewidth and maximum degree. We analyze the possibility of developing an efficient approximation algorithm and show that two heuristic algorithms proposed so far cannot have better than a logarithmic approximation guarantee. Finally, we prove that the problem does not admit better than a logarithmic approximation, unless P=NP.

AB - Diffusion on complex networks is often modeled as a stochastic process. Yet, recent work on strategic diffusion emphasizes the decision power of agents [1] and treats diffusion as a strategic problem. Here we study the computational aspects of strategic diffusion, i.e., finding the optimal sequence of nodes to activate a network in the minimum time. We prove that finding an optimal solution to this problem is NP-complete in a general case. To overcome this computational difficulty, we present an algorithm to compute an optimal solution based on a dynamic programming technique. We also show that the problem is fixed parameter-tractable when parametrized by the product of the treewidth and maximum degree. We analyze the possibility of developing an efficient approximation algorithm and show that two heuristic algorithms proposed so far cannot have better than a logarithmic approximation guarantee. Finally, we prove that the problem does not admit better than a logarithmic approximation, unless P=NP.

KW - Complex networks

KW - Influence maximization

KW - Network contagion

KW - Strategic diffusion

UR - http://www.scopus.com/inward/record.url?scp=85078763818&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2020.01.027

DO - 10.1016/j.tcs.2020.01.027

M3 - Article

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -