A new competitive algorithm for the counterfeit coin problem

Abstract

Consider a set of coins where each coin is either of a heavy type or a light type. The problem is to sort the coins (according to the type) by minimizing the number of weighings on a balance. The case that only one coin, called a counterfeit, has a different weight than the others is a classic mathematical puzzle. Later works study the case of more than one counterfeit, but the number of counterfeits is always assumed known. Recently, Hu and Hwang gave an algorithm that does not depend on the knowledge of the number of counterfeits, and yet performs uniformly well whatever that number turns out to be in the sample considered. Such an algorithm is known as a competitive algorithm and the uniform guarantee is measured by its competitive constant. In this paper we give a new and simple competitive algorithm whose competitive constant improves the existing one by a ratio of 2 3 .