Group Testing with Runlength Constraints for Topological Molecular Storage

Motivated by applications in topological DNA-based data storage, we introduce and study a novel setting of Non-Adaptive Group Testing (NAGT) with runlength constraints on the columns of the test matrix, in the sense that any two 1's must be separated by a run of at least d 0's. We describe and analyze a probabilistic construction of a runlength-constrained scheme in the zero-error and vanishing error settings, and show that the number of tests required by this construction is optimal up to logarithmic factors in the runlength constraint d and the number of defectives k in both cases. Our results reveal that runlength-constrained NAGT is not more restrictive than unconstrained NAGT when d = O(k), and that for almost all choices of d and k it is not more restrictive than NAGT with a column Hamming weight constraint only.