Efficient Parallel Computation of Nearest Neighbor Interchange Distances

TL;DR

This paper presents a parallel approximation algorithm for computing the nni-distance between phylogenetic trees, achieving logarithmic time complexity and near-optimal approximation ratios in the CRCW-PRAM model.

Contribution

It introduces an efficient parallel algorithm for nni-distance approximation with provable bounds, based on prior sequential methods.

Findings

Runs in O(log n) time with O(n) processors

Constructs nni-operation sequence with weight at most O(log n) times optimal

Identifies good edge-pairs in O(log n) time with O(n log n) processors

Abstract

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) \cdot 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 edge-pairs between two weighted phylogenies can be computed in O(log n) time on O(n log n) processors.