2009/01/21 by Leo van Iersel, van Iersel, Leo, Matthias Mnich +1
Biochemistry, Genetics and Molecular Biology · Computer Science · #Algorithms and Data Compression #Data Mining Algorithms and Applications #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Genomics and Phylogenetic Studies #cs.DM #cs.DS
paper · pdf · doi:10.48550/arxiv.0901.3299
This paper has been withdrawn by the authors due to an error
openalex publication_date 2009/01/21 · arxiv created 2010/05/28 · arxiv updated 2010/05/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A chief problem in phylogenetics and database theory is the computation of a maximum consistent tree from a set of rooted or unrooted trees. A standard input are triplets, rooted binary trees on three leaves, or quartets, unrooted binary trees on four leaves. We give exact algorithms constructing rooted and unrooted maximum consistent supertrees in time O(2n n5 m2 log(m)) for a set of m triplets (quartets), each one distinctly leaf-labeled by some subset of n labels. The algorithms extend to weighted triplets (quartets). We further present fast exact algorithms for constructing rooted and unrooted maximum consistent trees in polynomial space. Finally, for a set T of m rooted or unrooted trees with maximum degree D and distinctly leaf-labeled by some subset of a set L of n labels, we compute, in O(2mD nm m5 n6 log(m)) time, a tree distinctly leaf-labeled by a maximum-size subset X of L that all trees in T, when restricted to X, are consistent with.