  Cascades represent rapid changes in networks. A cascading phenomenon of
ecological and economic impact is the spread of invasive species in geographic
landscapes. The most promising management strategy is often biocontrol, which
entails introducing a natural predator able to control the invading population,
a setting that can be treated as two interacting cascades of predator and prey
populations. We formulate and study a nonlinear problem of optimal biocontrol:
optimally seeding the predator cascade over time to minimize the harmful prey
population. Recurring budgets, which typically face conservation organizations,
naturally leads to sparse constraints which make the problem amenable to
approximation algorithms. Available methods based on continuous relaxations
scale poorly, to remedy this we develop a novel and scalable randomized
algorithm based on a width relaxation, applicable to a broad class of
combinatorial optimization problems. We evaluate our contributions in the
context of biocontrol for the insect pest Hemlock Wolly Adelgid (HWA) in
eastern North America. Our algorithm outperforms competing methods in terms of
scalability and solution quality, and finds near optimal strategies for the
control of the HWA for fine-grained networks -- an important problem in
computational sustainability.
