On Sorting by Bounded Block Interchanges

TL;DR

This paper investigates a constrained version of the sorting by block interchanges problem, establishing its computational complexity and highlighting its significance in genomics applications.

Contribution

It introduces the problem of sorting by k-block interchanges, proves NP-hardness for k=1, and discusses the problem's complexity spectrum.

Findings

NP-hardness for k=1

Easy for k=n-1

Relevance to genomics applications

Abstract

In this work, we consider a restricted case of the well studied Sorting by Block Interchanges problem. We put an upper bound k on the length of the blocks (substrings) to be interchanged at each step. We call the problem Sorting by k-Block Interchanges. We show the problem to be NP-Hard for k=1. The problem is easy for k=n-1, where n is the length of the permutation (the unbounded case). Sorting by Block Interchanges is a very important and widely studied problem with applications in comparative genomics.