Sticky Seeding in Discrete-Time Reversible-Threshold Networks

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 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 Ω(ln(OPT ))-hard to approximate and that maximizing conversion subject to a budget is (1 − 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|) 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|) 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.