Abstract
The trace reconstruction problem is to reconstruct a string x of length n given m random subsequences where each subsequence is generated by deleting each character of x independently with probability p. Two natural questions are a) how large must m be as a function of n and p such that reconstruction is possible with high probability and b) how can this reconstruction be performed efficiently. Existing work considers the case when x is chosen uniformly at random and when x is arbitrary. In this paper, we relate the complexity of both cases; improve bounds by Holenstein et al. (SODA 2008) on the sufficient value of m in both cases; and present a significantly simpler analysis for some of the results proved by Viswanathan and Swaminathan (SODA 2008), Kannan and McGregor (ISIT 2005), and Batu et al. (SODA 2004). In particular, our work implies the first sub-polynomial upper bound (when the alphabet is polylogn) and super-logarithmic lower bound on the number of traces required when x is random and p is constant.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Batu, T., Kannan, S., Khanna, S., McGregor, A.: Reconstructing strings from random traces. In: ACM-SIAM Symposium on Discrete Algorithms, pp. 910–918 (2004)
Dudík, M., Schulman, L.J.: Reconstruction from subsequences. J. Comb. Theory, Ser. A 103(2), 337–348 (2003)
Holenstein, T., Mitzenmacher, M., Panigrahy, R., Wieder, U.: Trace reconstruction with constant deletion probability and related results. In: ACM-SIAM Symposium on Discrete Algorithms, pp. 389–398 (2008)
Kannan, S., McGregor, A.: More on reconstructing strings from random traces: Insertions and deletions. In: IEEE International Symposium on Information Theory, pp. 297–301 (2005)
Lember, J., Matzinger, H.: Standard deviation of the longest common subsequence. The Annals of Probability 37(3), 1192–1235 (2009)
Pollard, D.: Asymptopia (2000), http://www.stat.yale.edu/pollard/
Scott, A.D.: Reconstructing sequences. Discrete Mathematics 175(1-3), 231–238 (1997)
Viswanathan, K., Swaminathan, R.: Improved string reconstruction over insertion-deletion channels. In: ACM-SIAM Symposium on Discrete Algorithms, pp. 399–408 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
McGregor, A., Price, E., Vorotnikova, S. (2014). Trace Reconstruction Revisited. In: Schulz, A.S., Wagner, D. (eds) Algorithms - ESA 2014. ESA 2014. Lecture Notes in Computer Science, vol 8737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44777-2_57
Download citation
DOI: https://doi.org/10.1007/978-3-662-44777-2_57
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44776-5
Online ISBN: 978-3-662-44777-2
eBook Packages: Computer ScienceComputer Science (R0)