独立集的局部算法是半最优的
Local algorithms for independent sets are half-optimal
摘要：
我们发现，i.i.d.的因子的最大密度。当d趋于无穷大时，d-正则树上的独立集渐近地至多为（log d）/d。这与先前构造给出的下界相匹配。由此得出随机d-正则图上局部算法给出的最大独立集具有相同的渐近密度。相反，这些图上的最大独立集的密度是渐近2（log d）/d。我们还证明了类似的结果泊松-高尔顿-沃森树，稀疏Erdos-Renyi图上的局部算法产生的界限。
英文摘要：
We show that the largest density of factor of i.i.d. independent sets on the d-regular tree is asymptotically at most (log d)/d as d tends to infinity. This matches the lower bound given by previous constructions. It follows that the largest independent sets given by local algorithms on random d-regular graphs have the same asymptotic density. In contrast, the density of the largest independent sets on these graphs is asymptotically 2(log d)/d. We also prove analogous results for Poisson-Galton-Watson trees, which yield bounds for local algorithms on sparse Erdos-Renyi graphs.
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