Sticky Seeding in Discrete-Time Reversible-Threshold Networks

TL;DR

This paper studies the complexity of optimal seeding strategies in reversible-threshold networks with sticky interventions, providing hardness results and efficient evaluation methods for long-term impact in social network models.

Contribution

It introduces complexity bounds for network seeding problems with reversible behaviors and proposes efficient evaluation algorithms for long-term impact in sparse networks.

Findings

Converting a network at minimum cost is $ ext{Omega}( ext{ln}(OPT))$-hard to approximate.

Maximizing conversion under a budget is $(1-rac{1}{e})$-hard to approximate.

Long-term impact evaluation can be done in $O(|E|^2)$ operations for unweighted networks.

Abstract

When nodes can repeatedly update their behavior (as in agent-based models from computational social science or repeated-game play settings) the problem of optimal network seeding becomes very complex. For a popular spreading-phenomena model of binary-behavior updating based on thresholds of adoption among neighbors, we consider several planning problems in the design of \textit{Sticky Interventions}: when adoption decisions are reversible, the planner aims to find a Seed Set where temporary intervention leads to long-term behavior change. We prove that completely converting a network at minimum cost is $\Omega(\ln (OPT) )$-hard to approximate and that maximizing conversion subject to a budget is $(1-\frac{1}{e})$-hard to approximate. Optimization heuristics which rely on many objective function evaluations may still be practical, particularly in relatively-sparse networks: we prove that the long-term impact of a Seed Set can be evaluated in $O(|E|^2)$ operations. For a more descriptive model variant in which some neighbors may be more influential than others, we show that under integer edge weights from $\{0,1,2,...,k\}$ objective function evaluation requires only $O(k|E|^2)$ operations. These operation bounds are based on improvements we give for bounds on time-steps-to-convergence under discrete-time reversible-threshold updates in networks.