On minimizing testing rounds for fault identification

Abstract

A bound is obtained for the number of rounds of testing sufficient to identify the faulty units of a system. Within a single round each unit may participate in at most one test. The authors give an adaptive algorithm which works in O(log/sub (n/t)//sup t/) rounds and uses O(n) tests. The multiplicative constants in the new bounds are small; four in both cases. This is a major improvement over previous nonadaptive and adaptive algorithm which required O(t+log n) rounds of testing and O(n+t) tests. If t>n/sup 1- epsilon /, then the algorithm runs within a constant number of rounds.<>