关于最小广播图研究

广播是网络上信息的传播过程。在这个过程中一个结点将信息传给所有其他的结点。本文确定Ｂ（１９）的值。另外还给出Ｂ（２－＾ｋ－ｊ），ｊ＝１，２，３，４的下界，并确定Ｂ（２＾５－１）和Ｂ（２＾５－２）的值。     

最小谣传图的一个有效算法

谣传是信息网络中结点之间的一种常见的、重要的信息交换方式，在谣传过程中，每一个结点都得到ｋ个结点的信息，这个概念在计算机网络及其它信息、通信网络的设计中有着重要的意义，本文把“权”的概念引入到谣传问题中来，从而定义了最小谣传图，并给出了最小谣传图的一个好算法。     

UP,βn和FewP完全问题的相对同构性

本文引进相对的多项式化归和相对多一多项式同构等概念，对ＵＰ、βｎ的ＦｅｗＰ的相对完全集讨论它们的相对同构问题。并得到如下结果：１（１）对任何≤ｍ＾Ｐ，Ｂｎ－βｎ＾Ｂｎ完全集Ｃ，Ｃ≈Ｐ＾ＢｎＡｎ←→Ｃ为Ｐ＾Ｂｎ柱。（２）对任何≤ｍ＾Ｐ，Ｂ－ＦｅｗＰ＾Ｂ完全集Ｃ，Ｃ≈Ｐ＾Ｂ∪Ａｎ←→Ｃ为Ｐ＾Ｂ柱，其中Ｂ＝ＳＡＴ－∪Ａｎ。 ｎ∈Ｎ ｎ∈Ｎ     

论PANCAKE互连网的连通性

本详细地讨论了ｎ－Ｐａｎｃａｋｅ在栅去不超过２ｎ－４个结点时的连通情况，并由此给出ｎ－Ｐａｎｃａｋｅ的条件连通度和条件直径，从本可以看出，ｎ－Ｐａｎｃａｋｅ是一种具有很强连通性的较好的并行网络拓扑结构。     

4个多色Ramsey数的下界

研究了素数阶完全图Ｋｐ的边的ｎ－染色，给出了计算它的子图Ｇｐ（Ｓｉ）的团数的一种算法，得到１个三色，３个四色Ｒａｍｓｅｙ数的新的下界     

一类扩展的Steiner树优化问题及其应用

本文提出了一个计算机网络通信和分布式系统中的一类扩展的Ｓｔｅｉｎｅｒ树问题．对此问题设计了两个求其最优解的算法．这两个算法的时间复杂性分别是Ｏ（３（ｋ－１）·ｎ＋２（ｋ－１）·ｎ２）和Ｏ（２（ｎ－ｋ）·ｎ２）．其中，ｋ是一棵Ｓｔｅｉｎｅｒ树需支撑的给定顶点的个数．     

Z^＊pq中离散对数问题的安全谓词

本文讨论了Ｚ＾＊ｎ（ｎ＝ｐｑ，ｐ和ｑ未知）中离散对数问题的一些基本概念及问题本身的难度；定义了Ｚ＾＊ｎ中离散对数问题中关于判断主平方根的谓词Ｂｎ，ａ（ｘ），证明了谓词Ｂｎ，ａ（ｘ）即为Ｚ＾＊ｎ中离散对数问题的安全谓词。     

最小生成树的高效异步并行算法

在ＭＩＭＤ－ＳＭ并行计算模型上，本文给出了时间复杂性为Ｏ（ｎ（ｎ／ｐ＋ｌｏｇｐ））的最小生成树的异步并行算法，其中ｎ，ｐ（１≤ｐ≤ｎ）分别表示图的顶点数和处理机的个数。     

超立方网络上的平行路径

超立方是分布存储系中最常用的结构。在以往的工作中,人们已经提出了不少容错寻径算法,然而,还没有考虑Ｈｎ中│Ｆ│≥２ｎ－２的情形,在一个含有故障结点集Ｆ的ｎ维超立方网络Ｈｎ中,│Ｆ│≤４ｎ－２４,（ｓ０,ｄ０）,（ｓ１,ｄ１）是其中任意两对非故障结点,结果,（１）对↓Ａｖ∈Ｖ（Ｈｎ）,有│Ａ（ｖ,Ｈｎ－Ｆ）│≥６．（２）沿着某一维ｋ（０≤ｋ≤ｎ－１）,可将Ｈｎ分割成两部分：（ｄ０∈）Ｈｎ－１,０和（     

三族新的t-优图及关于t-优图的五个猜想的反例

得到了三族新的ｔ－优图,反证了Ｂｏｅａｃｈ等人提出了的关于ｔ－优图１０个猜想中的５个猜想,并提出４个新的猜想,比如以下的猜想不正确,若Ｇ是ｎ点ｅ的ｔ－优图,ｎ〈ｅ〈ｎ（ｎ－１）／２,则其连通度是（２ｅ／ｎ）代之以新的猜想,若Ｇ是ｎ点ｅ边ｔ－优图,则其边连通度λ（Ｇ）＝（２ｅ／ｎ）并且若λ（Ｇ）≥３,则Ｇ的一个边集是λ边割集当且仅当它关联于某个λ度顶点。     

泡形互连网络的条件连通性度量

n维泡形网络是设计大规模多处理机系统时最常用的互连网络拓扑结构之一,它以n维泡形图Bn为数学模型。F是连通图G的顶点子集,使得G-F不再连通且G-F的每个连通分支都有至少有n个顶点的F的势叫做G的Rk连通度。Rk连通度是衡量网络可靠性的一个重要参数。一般来说,网络的Rk连通度越大,其可靠性越高。研究了n维泡形网络的 k连通性;证明了在n维泡形网络中,当n≥3时,其R1连通度为2n-4;当n≥4 时,其R2连通度为4n-12。     

星型网络的3-限制边连通性

星型互连网络是并行与分布式处理领域中最流行的互连网络之一,它以n维星图作为拓扑结构。k-限制边连通度是衡量网络的可靠性的参数之一。一般来说,一个网络的k-限制边连通度越大,其连通性就越好。研究了星型互连网络的k限制边连通度;证明了当n≥3时,n维星型互连网络的3-限制连通度为3n－7。     

星网的4-限制边连通度

星网是并行与分布式处理系统中最流行的互连网络之一,它以n维星图作为拓扑结构。k-限制边连通度是衡量网络可靠性的重要参数之一;一般地,网络的k-限制边连通度越大,它的连通性就越好。研究了星网的k-限制边连通度,证明了当n≥4时,n维星网的4-限制连通度为4n－10。     

An O(k~2n~2) Algorithm to Find a k-Partition in a k-Connected Graph

Although there are polynomial algorithms of finding a 2-partition or a 3-partition for a simple undirected 2-connected or 3-connected graph respectively,there is no general algorithm of finding a k-partition for a k-connected graph G=(V,E),where k is the vertex connectivity of G.In this paper,an O(k^2n^2) general algorithm of finding a k-partition for a k-connected graph is proposed,where n=|V|.     

量子纠错码[[7,1,4]]_p(p>3)存在性的图论构造方法

利用由Schingemann和Werner两人提出的构造量子纠错码的图论方法,证明了量子纠错码[[7,1,4]]p(p>3)的存在性。     

Some Indices of Alphabet Overlap Graph

The undirected de Bruijn graph is often used as the model of communication network for its useful properties,such as short diameter,small maximum vertex degree.In this paper,we consider the alphabet overlap graph G(k,d,s): the vertex set V = {v|v = (v1 ...vk);vi ∈ {1,2,...,d},i = 1,2,...,k};they are distinct and two vertices u = (u1 ...uk) and v = (v1 ...vk) are adjacent if and only if us+i = vi or vs+i = ui (i = 1,2,...,k s).In particular,when s = 1,G(k,d,s) is just an undirected de Bruijn graph.First,we give a formula to calculate the vertex degree of G(k,d,s).Then,we use the corollary of Menger’s theorem to prove that the connectivity of G(k,d,s) is 2ds 2d2s k for s k/2.     

Random-tree Diameter and the Diameter-constrained MST

A minimum spanning tree (MST) with a small diameter is required in numerous practical situations such as when distributed mutual-exclusion algorithms are used, or when information retrieval algorithms need to compromise between fast access and small storage. The Diameter-Constrained MST (DCMST) problem can be stated as follows: given an undirected, edge-weighted graph, G , with n nodes and a positive integer, k , find a spanning tree with the smallest weight among all spanning trees of G which contain no path with more than k edges. This problem is known to be NP-complete, for all values of k ; 4 h k h ( n m 2). In this paper, we investigate the behavior of the diameter of an MST in randomly generated graphs. Then, we present heuristics that produce approximate solutions for the DCMST problem in polynomial time. We discuss convergence, relative merits, and implementation of these heuristics. Our extensive empirical study shows that the heuristics produce good solutions for a wide variety of inputs.     

An energy-efficient permutation routing protocol for single-hop radio networks

A radio network (RN) is a distributed system where each station or node is a small hand-held commodity device called a station. Typically, each station has access to a few channels for transmitting and receiving messages. By RN(p, k), we denote a radio network with p stations, where each station has access to k channels. In a single-hop RN, every station is within the transmission range of every other station. Each station consumes power while transmitting or receiving a message, even when it receives a message that is not destined for it. It is extremely important that the stations consume power only when it is necessary since it is not possible to recharge batteries when the stations are on a mission. We are interested in designing an energy-efficient protocol for permutation routing, which is one of the most fundamental problems in any distributed system. An instance of the permutation routing problem involves p stations of an RN, each storing n/p items. Each item has a unique destination address which is the identity of the destination station to which the item should be sent. The goal is to route all the items to their destinations while consuming as little energy as possible. We show that the permutation routing problem of n packets on an RN(p, k) can be solved in 2n/k+(p/k)/sup 2/+p+2k/sup 2/ slots and each station needs to be awake for at most 6n/p+2p/k+8k slots. When k/spl Lt/p/spl Lt/n, our protocol is more efficient, both in terms of total number of slots and the number of slots each station is awake compared to a previously published protocol by Nakano et al. (2001).     

L/sup p/ approximation of Sigma-Pi neural networks

A feedforward Sigma-Pi neural network with a single hidden layer of m neurons is given by /sup m//spl Sigma//sub j=1/c/sub j/g(n/spl Pi//sub k=1/x/sub k/-/spl theta//sub k//sup j///spl lambda//sub k//sup j/) where c/sub j/, /spl theta//sub k//sup j/, /spl lambda//sub k//spl isin/R. We investigate the approximation of arbitrary functions f: R/sup n//spl rarr/R by a Sigma-Pi neural network in the L/sup p/ norm. An L/sup p/ locally integrable function g(t) can approximate any given function, if and only if g(t) can not be written in the form /spl Sigma//sub j=1//sup n//spl Sigma//sub k=0//sup m//spl alpha//sub jk/(ln|t|)/sup j-1/t/sub k/.