Searching for faulty leaves in binary trees

Abstract

Let us be given a complete binary tree where an unknown subset of the leaves is faulty. Suppose that we can test any node whether there is a faulty leaf in the subtree routed at that node. Our aim is to give a strategy for finding all faults that minimizes the worst-case search length for a previously estimated number of faults. This question is of immediate interest in VLSI circuit checking. In this paper we give an elementary proof of the optimality of a very simple test strategy.