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The nearest-neighbor chain algorithm constructs a clustering in time proportional to the square of the number of points to be clustered. This is also proportional to the size of its input, when the input is provided in the form of an explicit distance matrix. The algorithm uses an amount of memory proportional to the number of points, when it is used for clustering methods such as Ward's method that allow constant-time calculation of the distance between clusters. However, for some other clustering methods it uses a larger amount of memory in an auxiliary data structure with which it keeps track of the distances between pairs of clusters.
The input to a clustering problem consists of a set of points.<ref name="murtagh-tcj"/> A ''cluster'' is any proper subset of the points, and a hierarchical clustering is a [[maximal element|maximal]] family of clusters with the property that any two clusters in the family are either nested or [[disjoint set|disjoint]].
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