An efficient search strategy for hidden ideals in pointed partially ordered sets

We consider a combinatorial question about searching for an unknown ideal μ within a known pointed poset λ. Elements of λ may be queried for membership in μ, but at most k positive queries are permitted. We provide a general search strategy for this problem, and establish new bounds (based on k and the degree and height of λ) for the total number of queries required to identify μ. We show that this strategy performs asymptotically optimally on the family of complete -ary trees as the height grows.