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

In this work, we study the one-sided block ordering problem under block-interchange distance. Given two signed permutations π and σ of size n, where π represents a partially assembled genome consisting of several blocks (i.e., contigs) and σ represents a completely assembled genome, the one-sided block ordering problem under block-interchange distance is to order (i.e., assemble) the blocks of π such that the block-interchange distance between the assembly of π and σ is minimized. 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 in algebra, we design an efficient algorithm to solve the one-sided block ordering problem under block-interchange distance in O(nlog⁡n) time. Moreover, we show that the assembly of π can be done in O(n) time and its block-interchange distance from σ can also be calculated in advance in O(n) time.