This algorithm is the most optimal way to implement agglomerative clustering. It reduces the naive implementation's runtime O($n^3$) to O($n^2$). It is detailed below :

1. Initalize all data points as Clusters
2. Initialize a stack K
3. While there are more than 1 clusters : a. If K is empty, add an arbitrary cluster to K b. Let A be K.top(). Find the cluster closest to A, say B. c. If B is already in K, it must have been added just before A (since it is closest to A). Thus, pop off A and B and merge them. d. If B is not already in K, add it to K.