A Multivariate Complexity Analysis of the Generalized Noah's Ark Problem

TL;DR

This paper analyzes the computational complexity of the Generalized Noah's Ark Problem, focusing on how various input parameters affect problem difficulty, and provides insights into its tractability and special cases.

Contribution

It offers a multivariate complexity analysis of the problem, identifying parameter regimes that influence computational hardness and exploring special cases.

Findings

Complexity depends on parameters like number of costs and survival probabilities.

Certain parameter restrictions lead to polynomial-time solvable cases.

The analysis guides future algorithm design for conservation planning.

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 a conservation project for each species 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 the complexity of 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|.