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In particular, we develop a lower bound (the RH bound) and an upper bound (the SIT bound) for the minimum reticulate network problem with multiple gene trees.
Full mode of the SIT bound: to test the performance of the bounds, we generate data with varying number of trees K, number of taxa n and level of reticulation r.
The general procedure of the SIT bound (for a fixed order) is as follows.
(ii) Computing the RH bound is often much faster and more scalable than the SIT bound.
The SIT bound is very accurate and also computable in practice for many datasets.
This suggests the current practical range of the full mode of the SIT bound.
In computing the SIT bound, PIRN can run full mode (slower but can give better results) or coarse mode (faster but less accurate).
On the high level, the upper bound performs stepwise insertion of trees into a reticulate network (and thus is called the SIT bound).
Coarse mode of the SIT bound: we also test the coarse mode of our methods for larger data, as described in Section 4.2.
The basic idea of the SIT bound is to reconstruct a reticulate network 𝒩 in a step-by-step way: 'insert' the given gene trees one by one into 𝒩 in some fixed order.
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