Reconstructing strings from random traces

We are given a collection of m random subsequences (traces) of a string t of length n where each trace is obtained by deleting each bit in the string with probability q. Our goal is to exactly reconstruct the string t from these observed traces. We initiate here a study of deletion rates for which we can successfully reconstruct the original string using a small number of samples. We investigate a simple reconstruction algorithm called Bitwise Majority Alignment that uses majority voting (with suitable shifts) to determine each bit of the original string. We show that for random strings t, we can reconstruct the original string (w.h.p.) for q = O(1/ log n) using only O(log n) samples. For arbitrary strings t, we show that a simple modification of Bitwise Majority Alignment reconstructs a string that has identical structure to the original string (w.h.p.) for q = O(1/n1/2+ ) using O(1) samples. In this case, using O(n log n) samples, we can reconstruct the original string exactly. Our ...

• Type: Conference
• Year: 2004
• Where: SODA
• Authors: Tugkan Batu, Sampath Kannan, Sanjeev Khanna, Andrew McGregor
• Keywords: Algorithms, Bitwise Majority Alignment, Original String, Small Number, SODA 2004