Exact and Approximation Algorithms for DNA Tag Set Design

TL;DR

This paper introduces new exact and approximation algorithms for designing DNA tag sets, including integer linear programming formulations and a novel cycle packing approach, significantly improving the number of tags generated.

Contribution

It presents the first ILP formulations for the problem and a new cycle packing method that enhances tag set size in DNA array design.

Findings

ILP formulations solve practical instances optimally

Cycle packing combined with tree search increases tags by over 40%

Periodic tags offer additional benefits in design

Abstract

In this paper we propose new solution methods for designing tag sets for use in universal DNA arrays. First, we give integer linear programming formulations for two previous formalizations of the tag set design problem, and show that these formulations can be solved to optimality for instance sizes of practical interest by using general purpose optimization packages. Second, we note the benefits of periodic tags, and establish an interesting connection between the tag design problem and the problem of packing the maximum number of vertex-disjoint directed cycles in a given graph. We show that combining a simple greedy cycle packing algorithm with a previously proposed alphabetic tree search strategy yields an increase of over 40% in the number of tags compared to previous methods.