A Lower Bound on the Number of Solutions to the Probed Partial Digest Problem

Abstract

The probed partial digestion mapping method partially digests a DNA strand with a restriction enzyme. A probe, which attaches to the DNA between two restriction enzyme cutting sites, is hybridized to the partially digested DNA, and the sizes of fragments to which the probe hybridizes are measured. The objective is to reconstruct the linear order of the restriction enzyme cutting sites from the multiset of measured lengths.In many cases, more than one underlying linear ordering is consistent with a multiset of measured lengths. This article shows that a multiset of N measured lengths can have as many as Ω( N t ) solutions for any t < ζ −1(2), where ζ( t) is the Riemann zeta function and ζ −1(2) ≍ 1.73.