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.

翻译：本文提出了在令牌滑动模型下，针对树和区间图中两个给定支配集之间计算最短重配置序列的新算法。在该问题中，给定一个图及其两个支配集，可将其视为放置在顶点上的令牌。目标在于找到将其中一个集合转化为另一个集合的最短支配集序列，其中序列中每个集合均由前一个集合中的单个令牌滑动得到。尽管识别任意序列的问题已得到充分研究，但本文首次针对支配集场景下的该优化变体提出了多项式时间算法。