On Independent Sets, 2-To-2 Games, And Grassmann Graphs
STOC '17: Symposium on Theory of Computing Montreal Canada June, 2017(2017)
摘要
We present a candidate reduction from the 30-Lin problem to the 2-to-2 Games problem and present a combinatorial hypothesis about Grassmann graphs which, if correct, is suffcient to show the soundness of the reduction in a certain non-standard sense. A reduction that is sound in this non-standard sense implies that it is NP-hard to distinguish whether an n-vertex graph has an independent set of size (1 - 1/root 2) n - o(n) or whether every independent set has size o(n), and consequently, that it is NP-hard to approximate the Vertex Cover problem within a factor root 2 - o(1).
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关键词
PCP,Vertex-Cover,Unique Games
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