SUBOPTIMALITY OF LOCAL ALGORITHMS FOR A CLASS OF MAX-CUT PROBLEMS
SUBOPTIMALITY OF LOCAL ALGORITHMS FOR A CLASS OF MAX-CUT PROBLEMS
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DOI：
10.1214/18-aop1291
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发表时间：
2019-05-01
影响因子：
2.3
通讯作者：
Rahman, Mustazee
中科院分区：
文献类型：
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作者：
Chen, Wei-Kuo;Gamarnik, David;Rahman, Mustazee
我们证明，在平均度为常数的随机K-一致超图中，对于偶数K >= 4，局部算法定义为独立同分布的因子当平均度足够大时，不能找到近似最大割。这些算法经常被用来获得随机图上最大割问题的下界，但不知道它们是否能成功地找到近似最大割。这一结果如下的事实，即重叠的任何两个几乎最大的削减在这样的超图不采取的值在一定的非平凡的区间称为重叠间隙属性的现象，这是通过比较稀释模型与适当的完全连接的自旋玻璃模型，并显示重叠间隙属性在后者的设置证明了大的平均度。
We show that in random K-uniform hypergraphs of constant average degree, for even K >= 4, local algorithms defined as factors of i.i.d. can not find nearly maximal cuts, when the average degree is sufficiently large. These algorithms have been used frequently to obtain lower bounds for the max-cut problem on random graphs, but it was not known whether they could be successful in finding nearly maximal cuts. This result follows from the fact that the overlap of any two nearly maximal cuts in such hypergraphs does not take values in a certain nontrivial interval-a phenomenon referred to as the overlap gap property-which is proved by comparing diluted models with large average degree with appropriate fully connected spin glass models and showing the overlap gap property in the latter setting.