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

Authors:
L. A. Newberg;D. Naor
Affiliations:
Univ Calif Berkeley, Dept Comp Sci, Berkeley, CA 94720, USA and Stanford Univ, Med Ctr, Dept Biochem, Stanford, CA 94305, USA;Univ Calif Berkeley, Dept Comp Sci, Berkeley, CA 94720, USA and Stanford Univ, Med Ctr, Dept Biochem, Stanford, CA 94305, USA
Venue:
Advances in Applied Mathematics
Year:
1993

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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 @W(N^t) solutions for any t