On clone assembly problems: an error-tolerant test for interval graphs

An important problem in DNA physical mapping is to reassemble the clone fragments to determine the structure of the entire molecule. The error-free version of this problem can be modeled as an interval graph recognition problem, where an interval graph is the intersection graph of a collection of intervals. However, since the data collected from laboratories almost surely contain some errors, traditional recognition algorithms can hardly be applied directly. We present a new test which has the following features: 1) the algorithm assembles the clones efficiently when the data is error-free; 2) in a case when the error rate is small (say, less than 3%) the test can likely detect and automatically correct the following three types of errors false positives, false negatives and chimeric clones; and 3) the test also identifies those parts of the data that are problematic, thus allowing biologists to perform further experiments to clean up the data.