We present a new class of metrics for unrooted phylogenetic X-trees inspired by the Gromov–Hausdorff distance for (compact) metric spaces. These metrics can be efficiently computed by linear or quadratic
rogramming. They are robust under NNI operations, too. The local behaviour of the metrics shows that they are different from any previously introduced metrics The performance of the metrics is briefly analysed on random weighted and unweighted trees as well as random caterpillars.

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