Multi-locus datasets are frequently used to infer phylogenies instead of using single locus. Missing data constitute a common challenge in such datasets as they can lead to stands, that is, sets of trees that are compatible with the incomplete per-locus trees. Under many common criteria the trees from one stand have identical score. Hence, identifying stands and determining their sizes is of crucial importance for a robust phylogenetic analysis. Recently, Chernomor et al. published Gentrius, a branch-and-bound algorithm that enumerates all stand trees given a set of unrooted incomplete locus trees. Despite its efficiency, the pattern and proportion of missing data in multi-locus datasets can still induce extremely long execution times.Here, we introduce the parallel version of the Gentrius algorithm. Our parallelization deploys a thread-pooling mechanism that maintains threads that finish early in busy-wait mode, such that they can contribute to solving long-running tasks. Thereby, we substantially reduce load imbalance and attain high parallel efficiency. Our performance assessment up to 16 cores yields linear parallel speedups on both, simulated, and empirical data. The parallel version of Gentrius is available as open source code under GNU GPL at https://github.com/togkousa/iqtree2/tree/terragen. All data we used for our analyses, are available for download at https://cme.h-its.oryexelixis/material/gentrius-parallel.tar.gz.

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