SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Discrete & Computational Geometry
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Approximation algorithms for NP-hard problems
A linear time algorithm for finding a k-tree core
Journal of Algorithms
Approximation algorithms for dispersion problems
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Hardness of Approximating Problems on Cubic Graphs
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
Linearly independent split systems
European Journal of Combinatorics
Efficient algorithms for the longest path problem
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Budgeted Phylogenetic Diversity on Circular Split Systems
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
An Approximation Algorithm for the Noah's Ark Problem with Random Feature Loss
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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In conservation biology it is a central problem to measure, predict, and preserve biodiversity as species face extinction. In 1992 Faith proposed measuring the diversity of a collection of species in terms of their relationships on a phylogenetic tree, and to use this information to identify collections of species with high diversity. Here we are interested in some variants of the resulting optimization problem that arise when considering species whose evolution is better represented by a network rather than a tree. More specifically, we consider the problem of computing phylogenetic diversity relative to a split system on a collection of species of size $n$. We show that for general split systems this problem is NP-hard. In addition we provide some efficient algorithms for some special classes of split systems, in particular presenting an optimal $O(n)$ time algorithm for phylogenetic trees and an $O(n\log n + n k)$ time algorithm for choosing an optimal subset of size $k$ relative to a circular split system.