## Spencer, Gwen - Sticky Seeding in Discrete-Time Reversible-Threshold Networks

dmtcs:1241 - Discrete Mathematics & Theoretical Computer Science, March 17, 2016, Vol. 18 no. 3
Sticky Seeding in Discrete-Time Reversible-Threshold Networks

Authors: Spencer, Gwen

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.

Source : oai:arXiv.org:1507.00691
Volume: Vol. 18 no. 3
Section: Distributed Computing and Networking
Published on: March 17, 2016
Submitted on: March 9, 2016
Keywords: Computer Science - Social and Information Networks

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