Fast FPT algorithms for computing rooted agreement forests: theory and experiments

Authors:
Chris Whidden;Robert G. Beiko;Norbert Zeh
Affiliations:
Faculty of Computer Science, Dalhousie University, Halifax, Nova Scotia, Canada;Faculty of Computer Science, Dalhousie University, Halifax, Nova Scotia, Canada;Faculty of Computer Science, Dalhousie University, Halifax, Nova Scotia, Canada
Venue:
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
Year:
2010

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Abstract

We improve on earlier FPT algorithms for computing a rooted maximum agreement forest (MAF) or a maximum acyclic agreement forest (MAAF) of a pair of phylogenetic trees. Their sizes give the subtree-prune-and-regraft (SPR) distance and the hybridization number of the trees, respectively. We introduce new branching rules that reduce the running time of the algorithms from O(3kn) and O(3kn logn) to O(2.42kn) and O(2.42kn logn), respectively. In practice, the speed up may be much more than predicted by the worst-case analysis. We confirm this intuition experimentally by computing MAFs for simulated trees and trees inferred from protein sequence data. We show that our algorithm is orders of magnitude faster and can handle much larger trees and SPR distances than the best previous methods, treeSAT and sprdist.