Shortest Dominating Set Reconfiguration under Token Sliding

TL;DR

This paper introduces the first polynomial algorithms for finding the shortest reconfiguration sequences between dominating sets in trees and interval graphs under the token sliding model, optimizing the transformation process.

Contribution

It presents novel polynomial algorithms for shortest dominating set reconfiguration under token sliding in trees and interval graphs, a problem not previously solved efficiently.

Findings

Developed polynomial algorithms for trees and interval graphs.

Achieved efficient computation of shortest reconfiguration sequences.

Extended understanding of dominating set reconfiguration complexity.

Abstract

In this paper, we present novel algorithms that efficiently compute a shortest reconfiguration sequence between two given dominating sets in trees and interval graphs under the Token Sliding model. In this problem, a graph is provided along with its two dominating sets, which can be imagined as tokens placed on vertices. The objective is to find a shortest sequence of dominating sets that transforms one set into the other, with each set in the sequence resulting from sliding a single token in the previous set. While identifying any sequence has been well studied, our work presents the first polynomial algorithms for this optimization variant in the context of dominating sets.