Sticky Seeding in Discrete-Time Reversible-Threshold Networks (original) (raw)

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))\Omega(\ln (OPT) )Omega(ln(OPT))-hard to approximate and that maximizing conversion subject to a budget is (1−frac1e)(1-\frac{1}{e})(1−frac1e)-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)O(|E|^2)O(∣E∣2) operations. For a more descript...