2-stage fault tolerant interval group testing

• Authors: Ferdinando Cicalese;José Augusto Amgarten Quitzau
• Venue: ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
• Year: 2007

We study the following fault tolerant variant of the interval group testing model: Given four positive integers n, p, s, e, determine the minimum number of questions needed to identify a (possibly empty) set P ⊆ {1, 2,..., n} (|P| ≤ p), under the following constraints. Questions have the form "Is I∩P ≠= Ø", where I can be any interval in {1, 2..., n}. Questions are to be organized in s batches of non-adaptive questions (stages), i.e, questions in a given batch can be formulated relying only on the information gathered with the answers to the questions in the previous batches. Up to e of the answers can be erroneous or lies. The study of interval group testing is motivated by several applications. remarkably, to the problem of identifying splice sites in a genome. In particular, such application motivates to focus algorithms that are fault tolerant to some degree and organize the questions in few stages, i.e., on the cases when s is small, typically not larger than 2. To the best of our knowledge, we are the first to consider fault tolerant strategies for interval group testing. We completely characterize the fully non-adaptive situation and provide tight bounds for the case of two batch strategies. Our bounds only differ by a factor of √11/10 for the case p = 1 and at most 2 in the general case.