Before revision:  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:  We present an algorithm that computes EMST(V) using O(S) in O}\big( (n^3 \log s /s^2) \log s\big) O(s) words of workspace.