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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 the above algorithm will return a hierarchy with suboptimal costs.<ref>{{
| last= Müllner
| first=Daniel
|
| title=Modern hierarchical, agglomerative clustering algorithms
| year=2011 }}.</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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