On the approximability of the Simplified Partial Digest Problem

In this paper, we analyse the computational complexity of an optimization version of the Simplified Partial Digest Problem (SPDP), which is a mathematical model for DNA mapping based on the results of a simplified partial digest experiment. We prove that recognizing 46.16% of the elements of the DNA map in the error-free simplified partial digest experiment is NP-hard in the strong sense. This implies that the problem of maximizing the number of correct elements of the DNA map in the error-free simplified partial digest experiment is pseudopolynomially non-approximable with the approximation ratio ρ=136.