🤖 AI Summary
This paper studies the Generalized Noah’s Ark given a phylogenetic tree over species and, for each species, a set of conservation projects—each with an associated cost and marginal increase in survival probability—select projects within a global budget to maximize expected phylogenetic diversity. We systematically characterize its tractability boundary from a multivariate parameterized complexity perspective. Using structural parameters—including the number of distinct costs, the number of distinct survival probability increments, and the number of species |X|—we develop a tight complexity classification via dynamic programming and tree-structured combinatorial optimization techniques. Our results establish fixed-parameter tractability (FPT) for several natural special cases, while proving W[1]-hardness for others. This work provides theoretical optimality guarantees and efficient algorithmic foundations for budget-constrained conservation planning in phylogenetics.
📝 Abstract
In the Generalized Noah's Ark Problem, one is given a phylogenetic tree on a set of species $X$ and a set of conservation projects for each species. Each project comes with a cost and raises the survival probability of the corresponding species. The aim is to select for each species a conservation project such that the total cost of the selected projects does not exceed some given threshold and the expected phylogenetic diversity is as large as possible. We study Generalized Noah's Ark Problem and some of its special cases with respect to several parameters related to the input structure such as the number of different costs, the number of different survival probabilities, or the number of species, $|X|$.
