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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. Therefore, when cluster distances are defined by a recursive formula (as some of the ones discussed above are), care must be taken so that they do not use the hierarchy in a way which is sensitive to merge order.<ref>{{citation
| last=Müllner
| first=Daniel
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