Connected dominating set (CDS) is a subset of vertices in a graph which dominates all vertices and induces a connected subgraph. This paper proposes a game theoretic approach to find a CDS, and proves that starting from a non-trivial initial state, every non-trivial Nash equilibrium is a minimal CDS and reaching a non-trivial Nash equilibrium needs $O(n)$ rounds in the worst case.

中文翻译：

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一种博弈论的方法，用于最小的连通支配集

连通支配集（CDS）是图形中顶点的子集，它支配所有顶点并生成连通子图。本文提出了一种寻找CDS的博弈论方法，并证明从一个非平凡的初始状态开始，每个非平凡的Nash均衡都是一个最小的CDS，并达到一个非平凡的Nash均衡需求$Ø（ñ）$ 在最坏的情况下四舍五入。