Minimum average congestion of enhanced and augmented hypercubes into complete binary trees

We study the embedding problem of enhanced and augmented hypercubes into complete binary trees. Using tree traversal techniques, we compute the minimum average edge congestion of enhanced and augmented hypercubes into complete binary trees.     

Multi-criteria robust design of a JIT-based cross-docking distribution center for an auto parts supply chain

We present a solution framework based on discrete-event simulation and enhanced robust design technique to address a multi-response optimization problem inherent in logistics management. The objective is to design a robust configuration for a cross-docking distribution center so that the system is insensitive to the disturbances of supply uncertainty, and provides steady parts supply to downstream assembly plants. In the proposed approach, we first construct a simulation model using factorial design and central composite design (CCD), and then identify the models that best describe the relationship between the simulation responses and system factors. We employ the response surface methodology (RSM) to identify factor levels that would maximize system potential.     

超立方机上一阶线性递推问题的并行求解

本文考察解一阶线性递推问题的三个并行算法在超立方机上的实现方案.通过给出原始数据与超立方机之间的适当的映射以及算法执行过程中数据的通讯方式,奇偶消元法、奇偶约简法和变间距二分法都可以在起立方机上有效地执行.文中给出了这些算法的复杂性结论.最后,为进一步减少通讯费用,我们提供了一种复杂性更小的新算法,其通讯时间是与问题规模无关的常数.     

Highly Symmetric Subgraphs of Hypercubes

Two questions are considered, namely (i) How many colors are needed for a coloring of the n-cube without monochromatic quadrangles or hexagons? We show that four colors suffice and thereby settle a problem of Erdös. (ii) Which vertex-transitive induced subgraphs does a hypercube have? An interesting graph has come up in this context: If we delete a Hamming code from the 7-cube, the resulting graph is 6-regular, vertex-transitive and its edges can be two-colored such that the two monochromatic subgraphs are isomorphic, cubic, edge-transitive, nonvertex-transitive graphs of girth 10.     

从设计到抽样

张润楚,王兆军（１９９６）提出了均匀设计抽样,将均匀设计变成抽样．本文给出一种由设计到抽样的一般方法,它可以将任何一个有优良均匀性的设计点集变成所有样本都有同样优良均匀性的抽样。     

抽样设计偏差的大样本性质

偏差（Ｄｉｓｃｒｅｐａｎｃｙ）作为布点设计均匀性的一个重要度量准则,已被使用很长时间,但对它的性质还研究得很不够．该文从模平移的方面系统地研究了偏差的性质,给出了在超立方体中一个布点设计按整体、大格子、小格子各种模平移的偏差大样本性质,这些性质对于计算机试验引进有关的设计和抽样方法起着重要的作用．     

立方体的线图的限制性连通度(英文)

子集SE(G)称为是图G的4-限制性边割,如果G-S不连通且每个连通分支至少有4个点.图G中基数最小的4-限制性边割称为4-限制性边连通度,记为λ4(G).本文确定了λ4(Qn)=4n-8.类似的,子集FV(G)称为图G的Rg-限制性点割,如果G-F不连通且每个连通分支的最小度不小于g.基数最小的Rg-限制性点割称为图G的Rg-限制性点连通度,记为κg(G).本文确定了κ1(L(Qn))=3n-4,κ2(L(Qn))=4n-8,其中L(Qn)是立方体的线图.     

An upper bound on the number of frequency hypercubes

A frequency n-cube $F^n(q;l_0,...,l_{m-1})$ is an n-dimensional q-by-...-by-q array, where $q=l_0+...+l_{m-1}$, filled by numbers $0,...,m-1$ with the property that each line contains exactly $l_i$ cells with symbol i, $i=0,...,m-1$ (a line consists of q cells of the array differing in one coordinate). The trivial upper bound on the number of frequency n-cubes is $m^{{(q-1)}^n}$. We improve that lower bound for $n>2$, replacing $q-1$ by a smaller value s, by constructing a testing set of size $s^n$ for frequency n-cubes (a testing set is a collection of cells of an array the values in which uniquely determine the array with given parameters). We also construct new testing sets for generalized frequency n-cubes, which are essentially correlation-immune functions in n q-valued arguments; the cardinalities of new testing sets are smaller than for testing sets known before.