08.03.2010

The nni-distance is a well-known distance measure for phylogenetic trees. We construct an efficient parrallel approximation algorithm (in the CRCW-PRAM model) for the nni-distance. Given two phylogenetic trees T₁ and T₂ on the same set of taxa and with the same multi-set of edge-weights, the algorithm constructs a sequence of nni-operations of weight at most O(log n) ⋅ opt, where opt denotes the minimum weight of a sequence of nni-operations transforming T₁ into T₂. This algorithm is based on the sequential approximation algorithm for the nni-distance given by DasGupta et al. [DHJ⁺00].