Trace reconstruction with constant deletion probability and related results

  • Authors:

  • Thomas Holenstein;Michael Mitzenmacher;Rina Panigrahy;Udi Wieder

  • Affiliations:

  • Microsoft Research, Silicon Valley;Harvard School of Engineering and Applied Sciences, Cambridge, MA;Microsoft Research, Silicon Valley;Microsoft Research, Silicon Valley

  • Venue:
  • Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
  • Year:
  • 2008

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Abstract

We provide several new results for the trace reconstruction problem. In this setting, a binary string yields a collection of traces, where each trace is independently obtained by independently deleting each bit with a fixed probability δ. Each trace therefore consists of a random subsequence of the original sequence. Given the traces, we wish to reconstruct the original string with high probability. The questions are how many traces are necessary for reconstruction, and how efficiently can the reconstruction be performed. Our primary result is that for some universal constant γ and uniformly chosen strings of length n, for any δ n) traces in poly(n) time with high probability. We also obtain algorithms that require a number of traces exponential in Õ (√n) for any δ