Sequencing by hybridization in few rounds

Sequencing by Hybridization (SBH) is a method for reconstructing an unknown DNA string based on obtaining, through hybridization experiments, whether certain short strings appear in the target string. Following Margaritis and Skiena (1995) 12], we study the SBH in rounds problem: The goal is to reconstruct an unknown string A (over a fixed alphabet) using queries of the form “does the string S appear in A?” for some query string S. The queries are performed in rounds, where the queries in each round depend on the answers to the queries in the previous rounds. We show that almost all strings of length n can be reconstructed in ${\log }^{1}n$ rounds with $O(n)$ queries per round. We also consider a variant of the problem in which for each substring query S, the answer is whether S appears once in the string A, appears at least twice in A, or does not appear in A. For this problem, we show that almost all strings can be reconstructed in 2 rounds of $O(n)$ queries. Our results improve the previous results of Margaritis and Skiena (1995) 12] and Frieze and Halldórsson (2002) 8].