Combinatorial Algorithms for Genome Rearrangements and DNA Oligonucleotide Arrays

Abstract This thesis concerns applications of combinatorial and algorithmic techniques in molecular biology. We focus on two main areas. In the first part we consider algorithms for tracing genome rearrangement events. Genome rearrangements are large scale DNA mutations, in which large segments are rearranged in order and orientation. Since these mutations are very rare, they are useful in evolutionary studies. In particular, we consider rearrangements in which a segment of DNA is cut out and inserted in a dierent,location in the same chromosome. If the segment is inserted in the same orientation it is called transposition; otherwise it is a transreversal. We first study the problem of sorting permutations by transpositions only. We develop a novel 1.5-approximation algorithm, that is considerably simpler than the extant ones. Moreover, the analysis of the algorithm is significantly less involved, and provides a good starting point for studying related open problems. Next, we consider the problem of sorting permutations by transpositions, transreversals and revrevs (an operation reversing each of two consecutive segments). Our main result is a quadratic 1.5-approximation algorithm for sorting by these operations, improving over the extant best known approximation ratio of 1.75. We present an implementation of both algorithms that runs in time O(n,/2