根图的稳定性及其优化
发布时间：2018-10-24 20:40
【摘要】：设灾难发生时,根图G的边以概率p独立幸存,则含根连通子图的顶点数的期望值EV(G;p)是根图的可靠性的合适指标.定义了子图的顶点数的平方期望值E2(G;p)后,则方差D(G;p)=E2(G;p)-[EV(G;p)]~2是根图稳定性的合适指标.推导得到了E2(G;p)的减-缩边公式,从而得到方差的一个递归计算方法.进而研究了一些特殊图的方差的计算公式.最后,结合期望和方差,讨论了根图的优化问题.
[Abstract]:If the edge of the root graph G survives independently by probability p when a disaster occurs, the expected value EV (Gupp) of the vertex number of the root connected subgraph is an appropriate index for the reliability of the root graph. After defining the square expectation value of the vertex number of a subgraph E _ 2 (G _ p), then the variance D (G _ p) = E _ 2 (G _ p)-[EV (Gupp)] ~ 2 is an appropriate index for the stability of the root graph. In this paper, the formula of reducing and shrinking edges of E2 (Gupp) is derived, and a recursive calculation method of variance is obtained. Furthermore, the formulas for calculating the variance of some special graphs are studied. Finally, the optimization problem of root graph is discussed by combining expectation and variance.
【作者单位】： 白城师范学院数学与统计学院;上海立信会计金融学院统计与数学学院;
【基金】：吉林省自然科学项目(20101564) 吉林省教育科学“十二五”规划重点自助课题(ZC12069)
【分类号】：O157.5
，
本文编号：2292497
[Abstract]:If the edge of the root graph G survives independently by probability p when a disaster occurs, the expected value EV (Gupp) of the vertex number of the root connected subgraph is an appropriate index for the reliability of the root graph. After defining the square expectation value of the vertex number of a subgraph E _ 2 (G _ p), then the variance D (G _ p) = E _ 2 (G _ p)-[EV (Gupp)] ~ 2 is an appropriate index for the stability of the root graph. In this paper, the formula of reducing and shrinking edges of E2 (Gupp) is derived, and a recursive calculation method of variance is obtained. Furthermore, the formulas for calculating the variance of some special graphs are studied. Finally, the optimization problem of root graph is discussed by combining expectation and variance.
【作者单位】： 白城师范学院数学与统计学院;上海立信会计金融学院统计与数学学院;
【基金】：吉林省自然科学项目(20101564) 吉林省教育科学“十二五”规划重点自助课题(ZC12069)
【分类号】：O157.5
，
本文编号：2292497
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