Handling long targets and errors in sequencing by hybridization
Proceedings of the sixth annual international conference on Computational biology
Reconstructing strings from substrings in rounds
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Open Combinatorial Problems in computational Molecular Biology
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Sequencing by hybridization in few rounds
Journal of Computer and System Sciences
Efficient reconstruction of RC-equivalent strings
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
A linear algorithm for string reconstruction in the reverse complement equivalence model
Journal of Discrete Algorithms
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We resolve two open problems presented in [8]. First, we consider the problem of reconstructing an unknown string T over a fixed alphabet using queries of the form “does the string S appear in T?” for some query string S. We show that Ω(ε−−1/2n2) queries are needed in order to reconstruct a 1–ε fraction of the strings of length n. This lower bound is asymptotically optimal since it is known that O(ε−−1/2n2) queries are sufficient. The second problem is reconstructing a string using queries of the form “does a string from $\mathcal{S}$ appear in T?”, where $\mathcal{S}$ is a set of strings. We show that a 1–ε fraction of the strings of length n can be reconstructed using O(n) queries, where the maximum length of a string in the queries is $2\log_{\sigma}n+\log_{\sigma}\frac{1}{\epsilon}+O(1)$. This construction is optimal up to constants.