An efficient algorithm for one-sided block ordering problem with block-interchange distance

Abstract

In this work, we study the one-sided block ordering problem with block-interchange distance. Given two signed permutations π and σ of size n, where π represents a partially assembled genome consisting of several blocks (contigs) and σ represents a completely assembled genome, the one-sided block ordering problem is to order (assemble) the blocks of π such that the block-interchange distance between the assembly of π and σ is minimized. In addition to genome rearrangements and phylogeny reconstruction, the one-sided block ordering problem is useful in genome resequencing, because its algorithms can be used to assemble the contigs of partially assembled resequencing genomes based on their completely assembled genomes. By using permutation groups, we design an efficient algorithm to solve the one-sided block ordering problem with block-interchange distance in time. Moreover, we show that the assembly of π can be done in time and its block-interchange distance from σ can also be calculated in advance in time. © 2013 Springer-Verlag Berlin Heidelberg.