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This analysis presents a search strategy for identifying hidden ideals in pointed posets, showing it performs asymptotically optimally as the height increases.
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.
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Roma Eisel (2025) studied this question.
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