In Chapter 3, we introduced the sequence assembly problem and discussed how to determine whether two fragments of a DNA sequence “overlap” when each may contain errors. In this chapter, we will consider how to use overlap information for a set of fragments to reassemble the original sequence. Of course, there is an infinite number of sequences that could give rise to a particular set of fragments. Our goal is to produce a reconstruction of the unknown source sequence that is reasonably likely to approximate the actual source well.

In Section 13.1 we will consider a model known as the shortest common superstring problem. This simple model assumes that our fragments contain no errors and that a short source sequence is more likely than a longer one. If the input set reflects the source exactly, then only exact overlaps between fragments are relevant to reconstruction. This approach's focus on exact matching allows us to use once more that extremely versatile data structure from Chapter 12, the suffix tree.

Beginning in Section 13.2, we consider another solution, a simplified version of the commonly used PHRAP program. PHRAP assumes that errors are present in the sequence files and furthermore that each base of each sequence is annotated with a quality value describing the level of confidence the sequencing machinery had in its determination of the base. It will not be possible to present all of the issues and options dealt with by PHRAP, but in Sections 13.3–13.7 we will present several important aspects of its approach in a Perl “mini-PHRAP”.