论文标题
分布式距离统治在图形中，没有$ k_ {2，t} $ - 次要
Distributed distance domination in graphs with no $K_{2,t}$-minor
论文作者
论文摘要
我们证明，一种简单的分布式算法发现了最佳距离的恒定近似值 - $ k $在图中占主导地位，而没有$ k_ {2，t} $ - binor。该算法以恒定数量的回合运行。我们进一步展示了该过程如何使用$ε> 0 $和$ k，t \ in \ mathbb {z}^+$在图中找到$ g =（v，e）$，而没有$ k_ {2，t} $ - minor t} $ - minter a-minor a-minor a-minor a-minor a-minor a-minor a-minor a-minor a-minor a-minor a-minor a-minor a-minor a-minor a-minor a-minor a-minor a-minor a-minor a dample-k $ to dime opt（1+（1+ε）$ aptem（1+ε）。该算法在本地模型中以$ o（\ log^*{| v |}）为单位运行。特别是，这两种算法都在外平面图中起作用。
We prove that a simple distributed algorithm finds a constant approximation of an optimal distance-$k$ dominating set in graphs with no $K_{2,t}$-minor. The algorithm runs in a constant number of rounds. We further show how this procedure can be used to give a distributed algorithm which given $ε>0$ and $k,t\in \mathbb{Z}^+$ finds in a graph $G=(V,E)$ with no $K_{2,t}$-minor a distance-$k$ dominating set of size at most $(1+ε)$ of the optimum. The algorithm runs in $O(\log^*{|V|})$ rounds in the Local model. In particular, both algorithms work in outerplanar graphs.
