Computational Aspects of Optimal Strategic Network Diffusion

TL;DR

This paper investigates the computational complexity of strategic network diffusion, proving NP-completeness, presenting an exact dynamic programming algorithm, and analyzing approximation limits.

Contribution

It introduces a dynamic programming approach for optimal activation sequences and analyzes the problem's fixed parameter tractability and approximation bounds.

Findings

Optimal solution computation is NP-complete.

A dynamic programming algorithm can find optimal solutions.

Heuristic algorithms cannot surpass logarithmic approximation guarantees.

Abstract

Diffusion on complex networks is often modeled as a stochastic process. Yet, recent work on strategic diffusion emphasizes the decision power of agents 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.