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On the duplication distance of binary strings

Alon, Noga and Bruck, Jehoshua and Farnoud, Farzad and Jain, Siddharth (2016) On the duplication distance of binary strings. In: 2016 IEEE International Symposium on Information Theory (ISIT). IEEE , Piscataway, NJ, pp. 260-264. ISBN 978-1-5090-1807-9.

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We study the tandem duplication distance between binary sequences and their roots. This distance is motivated by genomic tandem duplication mutations and counts the smallest number of tandem duplication events that are required to take one sequence to another. We consider both exact and approximate tandem duplications, the latter leading to a combined duplication/Hamming distance. The paper focuses on the maximum value of the duplication distance to the root. For exact duplication, denoting the maximum distance to the root of a sequence of length n by f(n), we prove that f(n) = Θ(n). For the case of approximate duplication, where a β-fraction of symbols may be duplicated incorrectly, we show using the Plotkin bound that the maximum distance has a sharp transition from linear to logarithmic in n at β = 1/2.

Item Type:Book Section
Related URLs:
URLURL TypeDescription DOIArticle
Bruck, Jehoshua0000-0001-8474-0812
Jain, Siddharth0000-0002-9164-6119
Additional Information:© 2016 IEEE. The authors would like to thank anonymous reviewers whose comments improved the presentation of this paper. This work was supported in part by the NSF Expeditions in Computing Program (The Molecular Programming Project), by a USA-Israeli BSF grant 2012/107, by an ISF grant 620/13, and by the Israeli I-Core program.
Funding AgencyGrant Number
Binational Science Foundation (USA-Israel)2012/107
Israel Science Foundation620/13
I-CORE Program of the Planning and Budgeting CommitteeUNSPECIFIED
Record Number:CaltechAUTHORS:20160824-101618060
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Official Citation:N. Alon, J. Bruck, F. Farnoud and S. Jain, "On the duplication distance of binary strings," 2016 IEEE International Symposium on Information Theory (ISIT), Barcelona, Spain, 2016, pp. 260-264. doi: 10.1109/ISIT.2016.7541301 URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69895
Deposited By: Tony Diaz
Deposited On:24 Aug 2016 21:42
Last Modified:22 Nov 2019 09:58

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