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基于存取结构与连通超图之间的关系,给出了顶点数为9,秩为3,超边数为4和5的一共226种不同构的连通超图存取结构,进而估算了它们的最优信息率。本文首先证明了具有4条超边的一类超星可以用理想的秘密共享方案来实现,并证明了满足一定条件的顶点数为n(5≤n≤11),超边数为5且秩为3的连通超图其最优信息率的下界为2/3。运用超图的相关理论对其中的16种超图存取结构最优信息率的精确值进行了计算,对余下的210种超图存取结构进行了分类,并估算了这些超图存取结构最优信息率的界。
Based on the relationship between access structures and connected hypergraphs, a total of 226 different connected hypergraph access structures with 9 vertices, 3 ranks, 4 and 5 hyperbolic edges are given, The optimal information rate. In this paper, we first prove that a class of super-stars with 4 super-edges can be realized by an ideal secret sharing scheme. It is also proved that the number of vertices satisfying certain conditions is n (5≤n≤11), the super-edge number is 5 and the rank is The lower bound of the optimal information rate of 3-connected hypergraph is 2/3. Using the theory of hypergraph, the exact values of the optimal information rates of the 16 kinds of hypergraph access structures are calculated and the remaining 210 kinds of hypergraph access structures are classified, and the estimation of these hypergraph access structures The best information rate of the world.