Constructing Evolutionary Trees - Algorithms and Complexity

Abstract: In this thesis three general problems concerning construction of evolutionary trees are considered. Algorithms for the problems are presented and the complexity of the problems is investigated. The thesis consists of three corresponding parts. The first part is devoted to the problem of constructing evolutionary trees in the experiment model. Different algorithms for the problem are given, including an optimal algorithm for constructing evolutionary trees and an optimal algorithm for merging two evolutionary trees. Matching lower bounds are also provided. The second part of the thesis presents results related to the inferred consensus tree problem. The optimization version of the problem is shown to be NP-complete and two heuristic algorithms are presented. Further, the ordered version of the problem is studied. In the last part of the thesis the complexity of the maximum homeomorphic subtree problem is examined. The problem is shown to be hard to approximate, unless P=NP, even for trees of constant height, whereas a constant approximation ratio is obtained in case of a constant number of trees of constant height.