An upper bound of the weight-balanced testing procedure with multiple testers

Abstract

Summary form only given, as follows. We investigate the performance of the weight-balanced testing algorithm (WBT) with multiple testers. The WBT has been proposed for coding, memory storage, search and testing applications. It aims to minimize the expected number of tests and often provides reasonable results if used with a single tester. However, the performance of the multiple-tester WBT, and particularly its upper bound, has not been analyzed before, despite the large body of literature that exists on the single-tester WBT, and recent papers that suggest it for testing applications. As we demonstrate, the multiple-tester WBT can be far from the optimal procedure. Our main objective is to generalize the upper bound on the expected number of tests that was obtained by Horbie (1977) for a single-tester WBT. For this purpose, we present the analogy between the WBT and alphabetic codes - both represented by the same Q-ary tree model. The upper bound is obtained on the expected path length of a Q-ary tree, which is constructed by the WBT.