Randomized Fast Design of Short DNA Words

TL;DR

This paper introduces a randomized polynomial-time algorithm for designing DNA code sets that satisfy specific constraints while minimizing string length, advancing the computational methods in DNA computing and self-assembly.

Contribution

It formulates the DNA code design as an optimization problem and provides the first polynomial-time algorithms with approximation guarantees for this task.

Findings

Algorithms run in polynomial time with high probability.

Output code lengths are within a constant factor of optimal.

First known approach to optimize DNA code design under these constraints.

Abstract

We consider the problem of efficiently designing sets (codes) of equal-length DNA strings (words) that satisfy certain combinatorial constraints. This problem has numerous motivations including DNA computing and DNA self-assembly. Previous work has extended results from coding theory to obtain bounds on code size for new biologically motivated constraints and has applied heuristic local search and genetic algorithm techniques for code design. This paper proposes a natural optimization formulation of the DNA code design problem in which the goal is to design n strings that satisfy a given set of constraints while minimizing the length of the strings. For multiple sets of constraints, we provide high-probability algorithms that run in time polynomial in n and any given constraint parameters, and output strings of length within a constant factor of the optimal. To the best of our knowledge, this work is the first to consider this type of optimization problem in the context of DNA code design.