Deterministic Polynomial-Time Algorithms for Designing Short DNA Words [article]

Ming-Yang Kao, Henry C. M. Leung, He Sun, Yong Zhang
2012 arXiv   pre-print
Designing short DNA words is a problem of constructing a set (i.e., code) of n DNA strings (i.e., words) with the minimum length such that the Hamming distance between each pair of words is at least k and the n words satisfy a set of additional constraints. This problem has applications in, e.g., DNA self-assembly and DNA arrays. Previous works include those that extended results from coding theory to obtain bounds on code and word sizes for biologically motivated constraints and those that
more » ... ied heuristic local searches, genetic algorithms, and randomized algorithms. In particular, Kao, Sanghi, and Schweller (2009) developed polynomial-time randomized algorithms to construct n DNA words of length within a multiplicative constant of the smallest possible word length (e.g., 9 maxlog n, k) that satisfy various sets of constraints with high probability. In this paper, we give deterministic polynomial-time algorithms to construct DNA words based on derandomization techniques. Our algorithms can construct n DNA words of shorter length (e.g., 2.1 log n + 6.28 k) and satisfy the same sets of constraints as the words constructed by the algorithms of Kao et al. Furthermore, we extend these new algorithms to construct words that satisfy a larger set of constraints for which the algorithms of Kao et al. do not work.
arXiv:1201.6358v1 fatcat:kgeqku5tijgc5i6ith65lzgkqm