On the number of SQSs,latin hypercubes and MDS codes

We establish that the logarithm of the number of latin d‐cubes of order n is and the logarithm of the number of sets of t ( is fixed) orthogonal latin squares of order n is . Similar estimations are obtained for systems of mutually strongly orthogonal latin d‐cubes. As a consequence, we construct a set of Steiner quadruple systems of order n such that the logarithm of its cardinality is as and .     

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.     

超立方体Q_n的传递剖分

一个图的传递剖分是它的边集的一个划分,且满足图的一个自同构群在其划分后的各个部分组成的集合上作用是传递的.决定了超立方体Q_n的所有G-传递剖分,其中G为Q_n的全自同构群.     

在计算机模拟试验中不同试验设计的比较

计算机模拟试验的设计与建模有许多方法,本文选择了四种不同类型的真模型,用四种试验设计方法,考虑了大小不同的试验方案,并选用了四种建模方法进行比较,给出一些经验性结论,相信这些结论在计算机试验中是有参考价值的。     

故障加强超立方体中的路和圈

本论文研究了含故障点的加强超立方体中路和圈的嵌入问题.利用数学归纳法,获得了故障加强超立方体中的路和圈,推广了超立方体中点容错路和圈嵌入的结果.     

Two-dimensional minimax Latin hypercube designs

We investigate minimax Latin hypercube designs in two dimensions for several distance measures. For the ?^∞-distance we are able to construct minimax Latin hypercube designs of n points, and to determine the minimal covering radius, for all n. For the ?¹-distance we have a lower bound for the covering radius, and a construction of minimax Latin hypercube designs for (infinitely) many values of n. We conjecture that the obtained lower bound is attained, except for a few small (known) values of n. For the ?²-distance we have generated minimax solutions up to n=27 by an exhaustive search method. The latter Latin hypercube designs are included in the website www.spacefillingdesigns.nl.     

Routing complexity of faulty networks

One of the fundamental problems in distributed computing is how to efficiently perform routing in a faulty network in which each link fails with some probability. This article investigates how big the failure probability can be, before the capability to efficiently find a path in the network is lost. Our main results show tight upper and lower bounds for the failure probability, which permits routing both for the hypercube and for the d‐dimensional mesh. We use tools from percolation theory to show that in the d‐dimensional mesh, once a giant component appears—efficient routing is possible. A different behavior is observed when the hypercube is considered. In the hypercube there is a range of failure probabilities in which short paths exist with high probability, yet finding them must involve querying essentially the entire network. Thus the routing complexity of the hypercube shows an asymptotic phase transition. The critical probability with respect to routing complexity lies in a different location than that of the critical probability with respect to connectivity. Finally we show that an oracle access to links (as opposed to local routing) may reduce significantly the complexity of the routing problem. We demonstrate this fact by providing tight upper and lower bounds for the complexity of routing in the random graph G_n,p. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Perfect 2-colorings of a hypercube

A coloring of the vertices of a graph is called perfect if the multiset of colors of all neighbors of a vertex depends only on its own color. We study the possible parameters of perfect 2-colorings of the n-dimensional cube. Some necessary conditions are obtained for existence of such colorings. A new recursive construction of such colorings is found, which produces colorings for all known and infinitely many new parameter sets.