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===Distances sensitive to merge order===
The above presentation explicitly disallowed distances sensitive to merge order. Indeed, allowing such distances can cause problems. In particular, there exist order-sensitive cluster distances which satisfy reducibility, but for which the above algorithm will return a hierarchy with suboptimal costs.<ref>{{citation
| last=
| first=Daniel
| arxiv=1109.2378v1
| title=Modern hierarchical, agglomerative clustering algorithms
| volume=1109
| pages=
| year=2011
| bibcode=2011arXiv1109.2378M }}.</ref> Following the earlier discussion of the value of defining cluster distances recursively (so that [[memoization]] can be used
to greatly speed up distance computations), care must be taken with recursively defined distances so that they are not using the hierarchy in a way which is sensitive to merge order.
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