两个局部模型中的最佳：局部集中式和局部分布式算法
Best of Two Local Models: Local Centralized and Local Distributed Algorithms
摘要：
我们考虑两种计算模型：集中式局部算法和局部分布式算法。一个模型中的算法适应于另一个模型以获得改进的算法。分布式顶点着色设计改进的集中式局部算法：最大独立集，最大匹配，最大（加权）匹配有界度图的近似计划。改进是三方面的：算法是确定性的、无状态的，并且探测器的数量在$\log^* n$中多项式增长，其中$n$是输入图的顶点数量。利用Nguyen和Onak的递归集中式局部改进技术\cite{onak2008}，得到了一种改进的最大（加权）匹配分布式近似方案。改进是双重的：我们减少了从$O(\log n)$到$O(\log^*n)$的轮数，并且我们的算法是确定性的而不是随机的。
英文摘要：
We consider two models of computation: centralized local algorithms and local distributed algorithms. Algorithms in one model are adapted to the other model to obtain improved algorithms. Distributed vertex coloring is employed to design improved centralized local algorithms for: maximal independent set, maximal matching, and an approximation scheme for maximum (weighted) matching over bounded degree graphs. The improvement is threefold: the algorithms are deterministic, stateless, and the number of probes grows polynomially in $\log^* n$, where $n$ is the number of vertices of the input graph. The recursive centralized local improvement technique by Nguyen and Onak~\cite{onak2008} is employed to obtain an improved distributed approximation scheme for maximum (weighted) matching. The improvement is twofold: we reduce the number of rounds from $O(\log n)$ to $O(\log^*n)$ for a wide range of instances and, our algorithms are deterministic rather than randomized.
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