דקל צור

Sequencing by Hybridization (SBH) is a method for reconstructing an unknown DNA string based on substring queries: Using hybridization experiments, one can determine for each string in a given set of strings, whether the string appears in the target string, and use this information to reconstruct the target string. We study the problem when the queries are performed in rounds, where the queries in each round depend on the answers to the queries in the previous rounds. We give an algorithm that can reconstruct almost all strings of length n using 2 rounds with O(n log_α n/log_α log _α n) queries per round, and an algorithm that uses log _α* n - Ω(1) rounds with O(n) queries per round, where a is the size of the alphabet. We also consider a variant of the problem in which for each substring query, the answer is whether the string appears once in the target, appears at least twice in the target, or does not appear in the target. For this problem, we give an algorithm that uses 3 rounds of O(n) queries. In all our algorithms, the lengths of the query strings are Θ(log_α n). Our results improve the previous results of Margaritis and Skiena [17] and Frieze and Halldórsson [10].