Tight Bounds for String Reconstruction Using Substring Queries

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 every non-adaptive algorithm must make Ω( −1/2 n2 ) queries in order to reconstruct a 1− fraction of the strings of length n. The second problem is reconstructing a string using queries of the form “does a string from S appear in T?”, where S is a set of strings. We show a non-adaptive reconstruction algorithm for this model which is optimal both in the number of queries, and in the length of the strings in the queries.

• Type: Conference
• Year: 2005
• Where: APPROX
• Authors: Dekel Tsur
• Keywords: Algorithms, APPROX 2005, Query String, String, Unknown String