The divisible load balance problem with shared cost and its application to phylogenetic inference

Motivated by load balance issues in parallel calculations of the phylogenetic likelihood function, we recently introduced an approximation algorithm for efficiently distributing partitioned alignment data to a given number of CPUs. The goal is to balance the accumulated number of sites per CPU, and, at the same time, to minimize the maximum number of unique partitions per CPU. The approximation algorithm assumes that likelihood calculations on individual alignment sites have identical runtimes and that likelihood calculation times on distinct sites are entirely independent from each other. However, a recently introduced optimization of the phylogenetic likelihood function, the so-called site repeats technique, violates both aforementioned assumptions. To this end, we modify our data distribution algorithm and explore 72 distinct heuristic strategies that take into account the additional restrictions induced by site repeats, to yield a ‘good’ parallel load balance. Our best heuristic strategy yields a reduction in required arithmetic operations that ranges between 2% and 92% with an average of 62% for all test datasets using 2, 4, 8, 16, 32, and 64 CPUs compared to the original site-repeat-agnostic data distribution algorithm.