Efficient Parallel Computation of Nearest Neighbor Interchange Distances

The nni-distance is a well-known distance measure for phylogenetic trees. We construct an efficient parallel approximation algorithm for the nni-distance in the CRCW-PRAM model running in O(log n) time on O(n) processors. 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. (2000). Furthermore, we show that the problem of identifying so called good edgepairs between two weighted phylogenies can be computed in O(log n) time on O(n logn) processors.