The complexity of ultrametric partitions on graphs
Information Processing Letters
SIAM Journal on Discrete Mathematics
Fast parallel recognition of ultrametrics and tree metrics
SIAM Journal on Discrete Mathematics
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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Constructing minimum ultrametric trees from distance matrices is an important problem in computational biology. In this paper, we examine its computational complexity and approximability. When the distances satisfy the triangle inequalities, we show that the minimum ultrametric tree problem can be approximated in polynomial time with error ratio 1.5(1 + ⌈log n⌉), where n is the number of species. We also developed an efficient branch and bound algorithm for constructing the minimum ultrametric tree for both metric and nonmetric inputs. The experimental results show that it can find an optimal solution for 25 species within reasonable time, while, to the best of our knowledge, there is no report of algorithms solving the problem even for 12 species.