Permutation Editing and Matching via Embeddings

Abstract. If the genetic maps of two species are modelled as permutations of (homologous) genes, the number of chromosomal rearrangements in the form of deletions, block moves, inversions etc. to transform one such permutation to another can be used as a measure of their evolutionary distance. Motivated by such scenarios, we study problems of computing distances between permutations as well as matching permutations in sequences, and finding most similar permutation from a collection (“nearest neighbor”). We adopt a general approach: embed permutation distances of relevance into well-known vector spaces in an approximately distance-preserving manner, and solve the resulting problems on the well-known spaces. Our results are as follows: – We present the first known approximately distance preserving embeddings of these permutation distances into well-known spaces. – Using these embeddings, we obtain several results, including the first known efficient solution for approximately...

• Type: Conference
• Year: 2001
• Where: ICALP
• Authors: Graham Cormode, S. Muthukrishnan, Süleyman Cenk Sahinalp
• Keywords: ICALP 2001, Permutation, Permutation Distances, Permutation Matching Problems, Programming Languages