Towards a DNA sequencing theory (learning a string)

Mathematical frameworks suitable for massive automated DNA sequencing and for analyzing DNA sequencing algorithms are studied under plausible assumptions. The DNA sequencing problem is modeled as learning a superstring from its randomly drawn substrings. Under certain restrictions, this may be viewed as learning a superstring in L.G. Valiant's (1984) learning model, and in this case the author gives an efficient algorithm for learning a superstring and a quantitative bound on how many samples suffice. A major obstacle to the approach turns out to be a quite well-known open question on how to approximate the shortest common superstring of a set of strings. The author presents the first provably good algorithm that approximates the shortest superstring of length n by a superstring of length O(n log n).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>