有向三环网络的六角环模型构造法  

The Hexagonal-loop Model of the Directed Triple-loop Networks

作　　者：邰伟鹏[1] 徐宏[1] 王小林[1] 

机构地区：[1]安徽工业大学计算机学院,安徽马鞍山243002

出　　处：《小型微型计算机系统》2014年第4期755-758,共4页Journal of Chinese Computer Systems

基　　金：国家自然科学基金青年科学基金项目(61003311)资助;安徽省高校自然科学研究重点项目(KJ2013Z023)资助;安徽省振兴计划项目(2013ZDJY073)资助

摘　　要：多环网络的直径是衡量网络效率的重要指标,提出一种新的有向三环网络TL(N;s1,s2,s3)(其中N=s1+s2+s3,s1≠s2≠s3,gcd(N;s1,s2,s3)=1)构造方法,得到其直观模型———六角环.研究并证明了六角环的一些性质,给出了有向三环网络直径d(N;s1,s2,s3)的显式公式.利用C#和SQL SERVER2008仿真出若干结果,实验结果显示该三环网络的构造方法实用有效.通过对仿真结果的分析,得到了一类特殊的三环网络TL(N;s1,s2,s3),当N=1+6(1+…+c),s1=c2,s2=(c+1)2,s3=N-s1-s2时,其直径d(N;s1,s2,s3)=2c,宽直径为d3(N;s1,s2,s3)=2c+2.该构造方法较传统的超L型瓦方法简单,又较三叉树构造法实用,在二维平面上就能得到一个简单、直观模型,并且仅需要分析环数c与位数pos这2个参数,就能求解出有向三环网络的直径.Based on the diameter of multi-loop networks is an important indicator to measure network efficiency, a new method to cal- culate the diameter of directed triple-loop networks TL { N; s1 , s2 , s3 ） （ N = s1 ＋ s2 ＋ s3 , s1 ,s2 , s3 , gcd （ N; s1 , s2 , s3 ） = 1 ） is presen- ted. A new diagram, hexagonal-loop, is obtained by this method. The attributes of hexagonal-loop were studied and the simple for- mula to express the diameter is presented. The structural model of hexagonal-loop is stimulated which makes use of C-Sharp and SQL Server2008. The experimental results show that the proposed approach is effective. A special kind of directed triple-loop networks TL （N;s1,s2,s3） was found. WhenN=1 ＋6（1 ＋… ＋c）,s1=c2, s2 = （c＋l）2, s3 =N-s1-s2,the diameterd（N;S1,S2,S3） =2c, the wide diameter d3 （ N; s1, s2 , s3 ） = 2c ＋ 2. The approach to construct the triple-loop networks is simpler than the traditional hyper L shape tile. In the meantime, it is more practical than the ternarytree. The diagram can be drawn in two dimensions and the diameter can be calculated only by two parameters. The diameter of directed triple-loop networks can be obtained by the two parameters, the loop number c and the position number pos.

关 键 词：有向三环网络 直径 六角环 仿真 

分 类 号：TP393[自动化与计算机技术—计算机应用技术]