@inproceedings{08c4ac5e4fb34261bd69e7628246ac22,

title = "Approximation algorithms for the fixed-topology phylogenetic number problem",

abstract = "In the ℓ-phylogeny problem, one wishes to construct an evolutionary tree for a set of species represented by characters, in which each state of each character induces no more than ℓ connected components. We consider the fixed-topology version of this problem for fixed-topologies of arbitrary degree. This version of the problem is known to be NP-complete for ℓ≥3 even for degree-3 trees in which no state labels more than ℓ+1 leaves (and therefore there is a trivial ℓ+1 phylogeny). We give a 2-approximation algorithm for all ℓ≥3 for arbitrary input topologies and we give an optimal approximation algorithm that constructs a 4-phylogeny when a 3-phylogeny exists. Dynamic programming techniques, which are typically used in fixed-toplogy problems, cannot be applied to ℓ-phylogeny problems. Our 2-approximation algorithm is the first application of linear programming to approximation algorithms for phylogeny problems. We extend our results to a related problem in which characters are polymorphic.",

author = "Mary Cryan and Goldberg, {Leslie Ann} and Phillips, {Cynthia A.}",

year = "1997",

doi = "10.1007/3-540-63220-4_56",

language = "English",

isbn = "978-3-540-63220-7",

volume = "1264",

series = "Lecture Notes in Computer Science",

publisher = "Springer Berlin Heidelberg",

pages = "130--149",

editor = "Alberto Apostolico and Jotun Hein",

booktitle = "Combinatorial Pattern Matching",

}