Project Final Report On Probe Interval Graphs

As a central problem in molecular biology, physical mapping is to find the relative positions of fragments of DNA along the genome using certain pairwise overlap information. Mathematical models are essential for designing efficient algorithms that construct, combine and refine maps. A widely used model is the interval graph. However, interval graph needs complete overlap information between DNA fragments, which is not always available. Sometimes we only have a subset of overlap information. For example, in cosmid contig mapping, a set of clones is placed on a filter for colony hybridization and the filter is probed with clones which have been radioactively labeled. This process produces overlap information as to which probes overlap with other clones. If only a subset of clones are used as probes, overlap information is not available between clones which are non-probes. Probe interval graph can be used when partial overlap information is available. In this report, we studied the characteristics of probe interval graphs. Then we analyzed an O(n) algorithm, proposed by Johnson and Spinrad [2001], which gives a possible solution to any probe interval graph. Based on our analysis, we gave an implementation of this algorithm, which can be used to build an application package to solve problems in physical mapping. In addition, the detailed aglorithm was illustrated step by step using two examples. The report is organized as follows. Section 2 gives some background knowledge of molecular biology and some relevant graph concepts. Section 3 presents a review of literatures. A characterization of probe interval graph is given in Section 4. Section 5-9 describe an O(n) algorithm to recognize whether a given graph is a probe interval graph using MD-PQ tree, an extension of MD-PQ tree. When the algorithm terminates with a positive