RECOMB '98 Proceedings of the second annual international conference on Computational molecular biology
Inferring evolutionary trees from ordinal data
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Recovering branches on the tree of life: an approximation algorithm
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
On the midpath tree conjuncture: a counter-example
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
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The problem of constructing trees given a matrix of interleaf distances is motivated by applications in computational evolutionary biology and linguistics. The general problem is to find an edge-weighted tree which most closely approximates (under some norm) the distance matrix. Although the construction problem is easy when the tree exactly fits the distance matrix, optimization problems under all popular criteria are either known or conjectured to be NP-complete. In this paper we consider the related problem where we are given a partial order on the pairwise distances, and wish to construct (if possible) an edge-weighted tree realizing the partial order. In particular we are interested in partial orders which arise from experiments on triples of species. We will show that the consistency problem is NP-hard in general, but that for certain special cases the construction problem can be solved in polynomial time.