Landscapes on spaces of trees

Authors:
Oliver Bastert;Dan Rockmore;Peter F. Stadler;Gottfried Tinhofer
Affiliations:
Zentrum Mathematik, TU München, D-80290 Muenchen, Germany;Department of Computer Science, Dartmouth College, 6211 Sudikoff Laboratory, Hanover, NH;Institut für Theoretische Chemie und Molekulare Strukturbiologie, Universität Wien, Währingerstraße 17, A-1090 Wien, Austria and The Santa Fe Institute, 1399 Hyde Park Road, Sa ...;Zentrum Mathematik, TU München, D-80290 Muenchen, Germany
Venue:
Applied Mathematics and Computation
Year:
2002

Citing 2
Cited 1

On the depth of combinatorial optimization problems

Discrete Applied Mathematics - Special issue: local optimization
Canonical approximation of fitness landscapes

Complexity

Walks in phylogenetic treespace

Information Processing Letters

Quantified Score

Hi-index	0.48

Visualization

Abstract

Combinatorial optimization problems defined on sets of phylogenetic trees are an important issue in computational biology, for instance the problem of reconstructing 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.