Rerooting Trees Increases Opportunities for Concurrent Computation and Results in Markedly Improved Performance for Phylogenetic Inference

Parallel computing algorithms benefit from increases in concurrency when the hardware capacity is being under utilized. For likelihood-based molecular evolution inferences this can be due to small problem sizes, or because hardware capacity has increased beyond dataset sizes. A central concept in this domain is a bifurcating tree, which represents evolutionary relationships. The topology of the tree being evaluated directly affects the degree of parallelism that can be exploited by likelihood-based algorithms. For time-reversible evolutionary models we can reroot an unbalanced tree in order to make it more symmetric, without affecting the likelihood. Based on the reduction in number of concurrent operation sets, we define a best-case theoretical expectations, based on tree size and topology, for speedup due to rerooting which approaches 2-fold as the number of tip nodes increases for pectinate trees, and much higher values for some random topologies as the number of tip nodes increases. Empirical results using the NVIDIA CUDA implementation of the BEAGLE library confirm the merit of this approach. For pectinate trees we observe speedups of up to 1.93-fold due to rerooting and even larger speedups for random trees for the core likelihood-evaluation function in BEAGLE.