Suppose we want to construct some structure on a bounded-degree graph, e.g., an almost maximum matching, and we want to decide about each edge depending only on its constant-radius neighborhood. We examine and compare the strengths of different extensions of these local algorithms. A common extension is to use preprocessing, which means that we can make some calculation about the whole graph, and each local decision can also depend on this calculation. In this paper, we show that preprocessing is needless: if a nearly optimal local algorithm uses preprocessing, then the same can be achieved by a local algorithm without preprocessing, but with a global randomization.

翻译：假设我们想要在有界度图上构造某种结构（例如近似最大匹配），并且希望每条边的决策仅依赖于其常数半径邻域。我们考察并比较了这些局部算法的不同扩展形式的能力。一种常见的扩展是使用预处理，即我们可以对整个图进行某些计算，而每个局部决策也可依赖于该计算结果。本文证明预处理并非必要：若一个近乎最优的局部算法使用了预处理，那么通过全局随机化，无需预处理的局部算法同样能实现相同效果。