European Journal of Combinatorics - Special issue on discrete metric spaces
Analyzing and visualizing sequence and distance data using SplitsTree
Discrete Applied Mathematics - Special volume on computational molecular biology
Inferring evolutionary trees with strong combinatorial evidence
Theoretical Computer Science - computing and combinatorics
A Fast Quartet tree heuristic for hierarchical clustering
Pattern Recognition
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The task of the quartet puzzling problem is to find a best-fitting binary X-tree for a finite n-set from confidence values for the 3n4 binary trees with exactly four leaves from X, its fitness being measured by the sum of the confidence values of all ''induced'' four-leaves subtrees. We describe a method for finding an exact solution of this problem by integer linear programming. Similar procedures can also be used for finding, e.g. best-fitting ''circular'' networks. A crucial problem in this context is, of course, how to obtain the input confidence values for the quartet trees. We propose to use inner products of rate-matrix diagonals calculated for pairs of taxa and present the trees resulting from applying our approach to two data sets of up to 36 mitochondrial sequences of mammals including an outgroup.