Before revision:  In addition, there is a read-write workspace of O(s ) words, where s \in \{1, \dots, n\} is a given parameter. In a time-space trade-off, we are interested in how the running time of an algorithm improves as s varies from 1 to n. We present a time-space trade-off for computing the Euclidean minimum spanning tree (EMST) of a set V of n sites in the plane. We present an algorithm that computes EMST(V) using O(S) in O}\big( (n^3 \log s /s^2) time and\big)  O(s) words of workspace.
After revision:  In addition, there is a read-write workspace of O(s ) words, where s \in \{1, \dots, n\} so that the algorithm may use O(s) cells of read-write memory (called the workspace) for its computations. Our goal is to find an algorithm that computes EMST(V) using O(S) in O}\big( (n^3 \log s /s^2) time and\big) O(s) words of workspace.