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Landscapes on Spaces of Trees

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  • Oliver Bastert
  • Dan Rockmore
  • Peter F. Stadler
  • Gottfried Tinhofer
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    Abstract

    Combinatorial optimization problems defined on sets of phylogenetic trees are an important issue in computational biology, for instance the problem of reconstruction a phylogeny using maximum likelihood or parsimony approaches. The collection of possible phylogenetic trees is arranged as a so-called Robinson graph by means of the nearest neighborhood interchange move. The coherent algebra and spectra of Robinson graphs are discussed in some detail as their knowledge is important for an understanding of the landscape structure. We consider simple model landscapes as well as landscapes arising from the maximum parsimony problem, focusing on two complementary measures of ruggedness: the amplitude spectrum arising from projecting the cost functions onto the eigenspaces of the underlying graph and the topology of local minima and their connecting saddle points.

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    Bibliographic Info

    Paper provided by Santa Fe Institute in its series Working Papers with number 01-01-006.

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    Date of creation: Jan 2001
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    Handle: RePEc:wop:safiwp:01-01-006

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    References

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    1. Fernando F. Feirreira & José F. Fontanari & Peter F. Stadler, 2000. "Landscape Statistics of the Low Autocorrelated Binary String Problem," Working Papers 00-07-033, Santa Fe Institute.
    2. Wim Hordijk & Peter F. Stadler, 1998. "Amplitude Spectra of Fitness Landscapes," Working Papers 98-02-021, Santa Fe Institute.
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    Cited by:
    1. Christoph Flamm & Ivo L. Hofacker & Peter F. Stadler & Michael T. Wolfinger, 2001. "Barrier Trees of Degenerate Landscapes," Working Papers 01-09-053, Santa Fe Institute.

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