Polynomial time algorithms for the token swapping problem on cographs

Abstract

The reconfiguration framework models the concept of transformation of combinatorial objects under a variety of operations and constraints. When it comes to reconfiguration challenges, the questions of importance are connectivity, diameter and distance, which can be considered and restrained in many ways. This work focuses on the Token Swap problem, a reconfiguration problem with variations that even precede the systematic study of the reconfiguration framework. In this problem, the goal is to convert an initial token placement on the vertices of a graph into a target token placement with the minimum number of swap operations. The main result of this paper is the construction of a polynomial algorithm for threshold graphs and subsequently cographs.