2017/07/13 by Yeow Meng Chee, Chee, Yeow Meng, Johan Chrisnata +5
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Advanced Data Storage Technologies #Algorithms and Data Compression #Combinatorics (math.CO) #DNA and Biological Computing #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1707.03956
openalex publication_date 2017/07/13 · arxiv created 2017/11/17 · arxiv updated 2017/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Tandem duplication in DNA is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain \em et al. (2016) proposed the study of codes that correct tandem duplications to improve the reliability of data storage. We investigate algorithms associated with the study of these codes. Two words are said to be ≤k-confusable if there exists two sequences of tandem duplications of lengths at most k such that the resulting words are equal. We demonstrate that the problem of deciding whether two words is ≤k-confusable is linear-time solvable through a characterisation that can be checked efficiently for k=3. Combining with previous results, the decision problem is linear-time solvable for k≤ 3. We conjecture that this problem is undecidable for k>3. Using insights gained from the algorithm, we study the size of tandem-duplication codes. We improve the previous known upper bound and then construct codes with larger sizes as compared to the previous constructions. We determine the sizes of optimal tandem-duplication codes for lengths up to twenty, develop recursive methods to construct tandem-duplication codes for all word lengths, and compute explicit lower bounds for the size of optimal tandem-duplication codes for lengths from 21 to 30.