TY - JOUR

T1 - Deterministic polynomial-time algorithms for designing short DNA words

AU - Kao, Ming-Yang

AU - Leung, Henry C.M.

AU - Sun, He

AU - Zhang, Yong

N1 - Funding Information:
First author was supported in part by NSF Grant CCF-1049899. Fourth author was supported in part by NSFC Grant 11171086.

PY - 2013/7/8

Y1 - 2013/7/8

N2 - 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 applied heuristic local searches, genetic algorithms, and randomized algorithms. In particular, Kao, Sanghi, and Schweller [16] 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×max{logn,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., 2.1logn+6.28k) and can 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.

AB - 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 applied heuristic local searches, genetic algorithms, and randomized algorithms. In particular, Kao, Sanghi, and Schweller [16] 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×max{logn,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., 2.1logn+6.28k) and can 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.

KW - DNA word design

KW - Derandomization

KW - Deterministic algorithms

UR - http://www.scopus.com/inward/record.url?scp=84879080194&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84879080194&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2012.12.030

DO - 10.1016/j.tcs.2012.12.030

M3 - Article

AN - SCOPUS:84879080194

SN - 0304-3975

VL - 494

SP - 144

EP - 160

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -