（弱）着色图的局部算法
Local algorithms in (weakly) coloured graphs
摘要：
本地算法是一种分布式算法，在恒定数量的同步通信轮之后完成。我们提出了2色图和弱2色图中最小支配集问题和最大匹配问题的局部近似算法。在弱2色图中，这两个问题都可以用近似因子$(Δ+1)/2$局部求解，其中$Δ$是图的最大度.我们还给出了一个匹配的下界证明，有没有一个更好的逼近因子，这些问题的局部算法。此外，我们表明，较强的假设2-着色没有帮助的情况下，支配集的问题，但有一个本地的近似计划的最大匹配问题的2-着色图。
英文摘要：
A local algorithm is a distributed algorithm that completes after a constant number of synchronous communication rounds. We present local approximation algorithms for the minimum dominating set problem and the maximum matching problem in 2-coloured and weakly 2-coloured graphs. In a weakly 2-coloured graph, both problems admit a local algorithm with the approximation factor $(Δ+1)/2$, where $Δ$ is the maximum degree of the graph. We also give a matching lower bound proving that there is no local algorithm with a better approximation factor for either of these problems. Furthermore, we show that the stronger assumption of a 2-colouring does not help in the case of the dominating set problem, but there is a local approximation scheme for the maximum matching problem in 2-coloured graphs.
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