Diagnosis-by-comparison is a realistic approach to the fault diagnosis of massive multicomputers. This paper addresses the fault identification of diagnosable multicomputer systems under the MM* comparison model. We find that the fault location task can be reduced to that under the classical PMC* model. On this basis, we present an O(n × Δ × δ) time diagnosis algorithm for an n-node MM* diagnosable system, where Δ and delta; denote the maximum and minimum degrees of a node, respectively. The proposed algorithm is much more efficient than the fastest known diagnosis algorithm (which consumes O(n) time) because realistic massive multi-computers are sparsely interconnected and hence Δ, δ < < n.