## Abstract

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^{-1/2}n^{2}) 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^{1/2}n^{2}) queries are sufficient. 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 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_{σ} n + log_{σ} 1/ε + O(1). This construction is optimal up to constants.

Original language | English |
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Pages (from-to) | 448-459 |

Number of pages | 12 |

Journal | Lecture Notes in Computer Science |

Volume | 3624 |

DOIs | |

State | Published - 1 Jan 2005 |

Externally published | Yes |

Event | 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and 9th International Workshop on Randomization and Computation, RANDOM 2005 - Berkeley, CA, United States Duration: 22 Aug 2005 → 24 Aug 2005 |