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.
This work was partly supported by ESPRIT LTR Project no. 20244 — ALCOM-IT.
Part of this work took place during a visit to Sandia National Laboratories which was supported by University of Warwick Research and Teaching Innovations Grant 0951CSA and by the U.S. Department of Energy under contract DE-AC04-94AL85000. Part of this work was supported by ESPRIT LTR Project no. 20244 — ALCOM-IT.
This work was performed under U.S. Department of Energy contract number DE-AC04-76AL85000.
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Cryan, M., Goldberg, L.A., Phillips, C.A. (1997). Approximation algorithms for the fixed-topology phylogenetic number problem. In: Apostolico, A., Hein, J. (eds) Combinatorial Pattern Matching. CPM 1997. Lecture Notes in Computer Science, vol 1264. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63220-4_56
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DOI: https://doi.org/10.1007/3-540-63220-4_56
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