Tractability results for the Double-Cut-and-Join circular median problem

TL;DR

This paper investigates the computational complexity of the circular median problem in genome rearrangement, showing it is tractable under certain fixed conditions related to the structure of the input genomes.

Contribution

The paper proves that the circular median problem becomes tractable when the number of degree-3 vertices in the breakpoint graph is fixed.

Findings

NP-complete in general

Tractable when degree-3 vertices are fixed

Provides new algorithms for special cases

Abstract

The circular median problem in the Double-Cut-and-Join (DCJ) distance asks to find, for three given genomes, a fourth circular genome that minimizes the sum of the mutual distances with the three other ones. This problem has been shown to be NP-complete. We show here that, if the number of vertices of degree 3 in the breakpoint graph of the three input genomes is fixed, then the problem is tractable