计算机科学 ›› 2021, Vol. 48 ›› Issue (4): 43-48.doi: 10.11896/jsjkx.201100139

• 计算机科学理论 • 上一篇    下一篇

(n,k)-冒泡排序网络的子网络可靠性

冯凯, 马鑫玉   

  1. 山西大学计算机与信息技术学院 太原030006
  • 收稿日期:2020-06-24 修回日期:2021-01-10 出版日期:2021-04-15 发布日期:2021-04-09
  • 通讯作者: 冯凯(fengkai@sxu.edu.cn)
  • 基金资助:
    国家自然科学基金(61502286)

Subnetwork Reliability of (n,k)-bubble-sort Networks

FENG Kai, MA Xin-yu   

  1. School of Computer and Information Technology,Shanxi University,Taiyuan 030006,China
  • Received:2020-06-24 Revised:2021-01-10 Online:2021-04-15 Published:2021-04-09
  • About author:FENG Kai,born in 1987,Ph.D,associate professor,master supervisor,is a member of China Computer Federation.His main research interests include fault-tolerance of interconnection network,graph theory and its applications.
  • Supported by:
    National Natural Science Foundation of China(61502286).

摘要: 并行计算机系统互连网络的拓扑性质对系统功能的实现起着重要的作用。为了精确度量基于(n,k)-冒泡排序网络构建的并行计算机系统的子网络容错能力,建立了(n,k)-冒泡排序网络中(n-m,k-m)-冒泡排序子网络与特定字符串之间的一一对应关系,研究了点故障模型下(n,k)-冒泡排序网络中(n-m,k-m)-冒泡排序子网络的可靠性。当2≤k≤n-2,1≤m≤k-1时,首先在概率故障条件下给出了(n,k)-冒泡排序网络中存在无故障的(n-m,k-m)-冒泡排序子网络的概率估计,并通过仿真实验验证了所得结果的精确性;其次,得出了不同数目的(n-m,k-m)-冒泡排序子网络保持无故障状态的平均失效时间的计算公式,仿真实验表明理论结果与仿真结果趋于一致。

关键词: (n,k)-冒泡排序网络, 并行计算机系统, 概率故障, 互连网络, 平均失效时间, 子网络可靠性

Abstract: Topological properties of the interconnection network of a parallel computer system play an important role in realizing functions of the system.In order to measure the fault tolerance abilities of subnetworks in the parallel computer system which is built based on the (n,k)-bubble-sort network,the one-to-one relation between (n-m,k-m)-bubble-sort subnetworks of the (n,k)-bubble-sort network and specific strings is constructed,and the reliability of (n-m,k-m)-bubble-sort subnetworks in the (n,k)-bubble-sort network is studied under the node fault model.Assuming that 2≤k≤n-2 and 1≤m≤k-1,the probability that at least one (n-m,k-m)-bubble-sort subnetwork is fault-free in an (n,k)-bubble-sort network under the probabilistic fault condition is firstly given,and the simulation experiments demonstrate the accuracy of the given results.Then the calculation formula of the mean time to failure to maintain the fault-free status of different number of (n-m,k-m)-bubble-sort subnetworks is obtained,and the theoretical results are shown to be in accordance with the simulation results.

Key words: (n, Interconnection network, k)-bubble-sort network, Mean time to failure, Parallel computer system, Probabilistic failure, Subnetwork reliability

中图分类号: 

  • TP393.02
[1]CHANG Y,BHUYAN L N.A combinatorial analysis of subcube reliability in hypercube[J].IEEE Transactions on Compu-ters,1995,44(7):952-956.
[2]LIN L,XU L,ZHOU S,et al.The reliability of subgraphs in the arrangement graph[J].IEEE Transactions on Reliability,2015,64(2):807-818.
[3]LI X,ZHOU S,XU X,et al.The reliability analysis based on subsystems of (n,k)-star graph[J].IEEE Transactions on Reliability,2016,65(4):1700-1709.
[4]KUNG T L,TENG Y H,LIN C K,et al.Combinatorial analysisof the subsystem reliability of the split-star network[J].Information Sciences,2017,415:28-40.
[5]FENG K,JI Z,WEI W.Subnetwork reliability analysis in k-ary n-cubes[J].Discrete Applied Mathematics,2019,267:85-92.
[6]ABRAHAM S,PADMANABHAN K.Reliability of the hypercube[C]//Proceedings of the 1988 International Conference on Parallel Processing.Piscataway:IEEE,1988:90-94.
[7]ZHOU S,LI X,LI J,et al.Reliability assessment of multiprocessor system based on (n,k)-star network[J].IEEE Transactions on Reliability,2017,66(4):1025-1035.
[8]LV M,ZHOU S,SUN X,et al.Reliability evaluation of datacenter network DCell[J].Parallel Processing Letters,2018,28(4):1850015.
[9]FENG K,LI J.Reliability assessment of k-ary n-cube networks[J].Journal of Computer Applications,2019,39(11):3323-3327.
[10]SHAWASH N.Relationships among popular interconnectionnetworks and their common generalization[D].Oakland:Oakland University,2008.
[11]CHENG E,LIPTÁK L,SHERMAN D.Matching preclusion for the (n,k)-bubble-sort graphs[J].International Journal of Computer Mathematics,2010,87(11):2408-2418.
[12]YANG Y X,QIU Y N.Sub-network preclusion in(n,k)-bubble-sort networks[J].Computer Science,2017,44(11):264-267.
[13]ZHAO S,HAO R,WU L.The generalized connectivity of (n,k)-bubble-sort graphs[J].The Computer Journal,2019,62(9):1277-1283.
[14]ZHAO S,HAO R.The fault tolerance of(n,k)-bubble-sort networks[J].Discrete Applied Mathematics,2020,285:204-211.
[15]BONDY J A,MURTY U S R.Graph Theory[M].New York:Springer,2008:1-356.
[16]SANE S.Combinatorial Techniques[M].New Delhi:Hindustan Book Agency,2016:57-79.
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