The median-of-longest-side rule chooses to split along the longest side of the node. On this axis it chooses to split at the median of the contained points.
Tree depth is bounded by log2(n).
The tree satisfies a packing lemma which guarantees good worst-case performance on approximate nearest neighbors searching and approximate range searching.
There are quite many thin nodes. This is the price to pay for the guaranteed logarithmic depth.
Because of the previous, in practice this rule results in slower performance than the sliding midpoint rule.
K-D Trees Are Better when Cut on the Longest Side, Matthew Dickerson, Christian A. Duncan, and Michael T. Goodrich, Proceedings of the 8th Annual European Symposium on Algorithms, 2000.