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.Comment: To appear at FCT 2023 (Fundamentals of Computation Theory