Online Abelian Pattern Matching

Ejaz T, Rahmann S, Stoye J. Online Abelian Pattern Matching. Forschungsberichte der Technischen Fakultät, Abteilung Informationstechnik / Universität Bielefeld. Bielefeld: Technische Fakultät der Universität Bielefeld; 2008.An abelian pattern describes the set of strings that comprise of the same combination of characters. Given an abelian pattern P and a text T [Epsilon] [Sigma]^n, the task is to find all occurrences of P in T, i.e. all substrings S = T_i...T_j such that the frequency of each character in S matches the specified frequency of that character in P. In this report we present simple online algorithms for abelian pattern matching, and give a lower bound for online algorithms which is [Omega](n)

2-Stage Fault Tolerant Interval Group Testing

Cicalese F, Quitzau JAA. 2-Stage Fault Tolerant Interval Group Testing. Forschungsberichte der Technischen Fakultät, Abteilung Informationstechnik / Universität Bielefeld. Bielefeld: Universität Bielefeld, Technische Fakultät; 2007

2-Stage Fault Tolerant Interval Group Testing

Cicalese F, Amgarten Quitzau JA. 2-Stage Fault Tolerant Interval Group Testing. In: Tokuyama T, ed. Algorithms and Computation. 18th International Symposium, ISAAC 2007, Sendai, Japan, December 17-19, 2007. Proceedings. Lecture notes in computer science, 4835. 2007: 858-868

2-Stage Fault Tolerant Interval Group Testing

Abstract. We study the following fault tolerant variant of the interval group testing model: Given three positive integers n, p,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 � = ∅?”, where I can be any interval in {1, 2..., n}. Up to e of the answers can be erroneous or lies. Questions are to be organized in batches of non-adaptive questions. Therefore, questions in a given batch can be formulated relying only on the information gathered with the answers to the questions in the previous batches. The study of interval group testing is motivated by several applications. Among others, it has applications to the problem of identifying splice sites in a genome. 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.