• Journal of KIISE:Computer Systems and Theory
• /
• v.29 no.12
• /
• pp.665-679
• /
• 2002

The fault diameter of a graph G is the maximum of lengths of the shortest paths between all two vertices when there are $\chi$(G) - 1 or less faulty vertices, where $\chi$(G) is connectivity of G. In this paper, we analyze the fault diameter of recursive circulant $G(2^m,2^k)$ with $k{\geq}3$. Let $ dia_{m.k}$ denote the diameter of $G(2^m,2^k)$. We show that if $2{\leq}m,2{\leq}k, the fault diameter of $G(2{\leq}m,2{\leq}k)$ is equal to $2^m-2$, and if m=k+1, it is equal to $2^k-1$. It is also shown that for m>k+1, the fault diameter is equal to di a_$m{\neq}1$(mod 2k); otherwise, it is less than or equal to$dia_{m.k+2}$.

• Journal of KIISE:Computer Systems and Theory
• /
• v.34 no.5_6
• /
• pp.176-186
• /
• 2007

An interconnection network can be represented as a graph where a vertex corresponds to a node and an edge corresponds to a link. The diameter of an interconnection network is the maximum length of the shortest paths between all pairs of vertices. The fault diameter of an interconnection network G is the maximum length of the shortest paths between all two fault-free vertices when there are $_k(G)-1$ or less faulty vertices, where $_k(G)$ is the connectivity of G. The fault diameter of an R-regular graph G with diameter of 3 or more and connectivity ${\tau}$ is at least diam(G)+1 where diam(G) is the diameter of G. We show that the fault diameter of a 2-dimensional $m{\times}n$ torus with $m,n{\geq}3$ is max(m,n) if m=3 or n=3; otherwise, the fault diameter is equal to its diameter plus 1. We also show that in $d({\geq}3)$-dimensional $k_1{\times}k_2{\times}{\cdots}{\times}k_d$ torus with each $k_i{\geq}3$, there are 2d mutually disjoint paths joining any two vertices such that the lengths of all these paths are at most diameter+1. The paths joining two vertices u and v are called to be mutually disjoint if the common vertices on these paths are u and v. Using these mutually disjoint paths, we show that the fault diameter of $d({\geq}3)$-dimensional $k_1{\times}k_2{\times}{\cdots}{\times}k_d$ totus with each $k_i{\geq}3$ is equal to its diameter plus 1.

• The Transactions of the Korea Information Processing Society
• /
• v.4 no.8
• /
• pp.1930-1939
• /
• 1997

In this paper, we analyze the fault diameter and fault tolerance of Gray cube proposed recently in [12]. fault diameter of an interconnection network is one of the important network measures concerning the distance between nodes when some nodes fail. It is showed that fault diameter of n-dimensional Gray cube having $2^n$ nodes is [(n+1)/2]+2, ($n{\ge}3$). It means the increment of the longest distance between nodes under node-failure is only constant factor. Comparing the result with the fault diameter of well-known hypercube, the longest routing distance of a message in a Gray cube under node-failure is about the half of that hypercube.

• The KIPS Transactions:PartA
• /
• v.17A no.1
• /
• pp.1-8
• /
• 2010

The fault diameter is one of the important measures for transmission rate and reliability of interconnection network. H.-O. Lee et al.[Parallel paths in folded hyper-star graph, Journal of KIPS, Vol.6, No.7, pp.1756-1769, 1999] suggested the node-disjoint paths of FHS (2n,n), and proved that the fault diameter of FHS(2n,n) is less than 2n-1. In this paper, we suggest an advanced node-disjoint paths of FHS(2n,n). We also prove that the wide diameter of FHS(2n,n) is dist(U,V)+4, and the fault diameter of FHS(2n,n) is less than n+2.

• The KIPS Transactions:PartA
• /
• v.12A no.6 s.96
• /
• pp.499-506
• /
• 2005

Recently, Hyper-Star network HS(m,k) which improves the network cost of hypercube has been proposed. In this paper, we show that the bisection width of regular Hyper-Star network HS(2n,n) is maximum (2n-2,n-1). Using the concept of container, we also show that k-wide diameter of HS(2n,n) is less than dist(u,v)+4, and the fault diameter is less than D(HS(2n,n))+2, where dist(u,v) is the shortest path length between any two nodes u and v in HS(2n,n), and D(HS(2n,n)) is its diameter.

• Proceedings of the Korean Information Science Society Conference
• /
• 2001.10a
• /
• pp.589-591
• /
• 2001

본 논문에서는 재귀원형군 G(2$^{m}$ , 2$^{k}$ )에서 노드에 고장이 났을 경우 임의의 두 노드사이의 고장이 없는 최단경로의 길이를 분석한다. m > k+1인 G(2$^{m}$ , 2$^{k}$ )에서 m = nk+r이라 하자. 여기서 n $\geq$ 이고, 1$\leq$ r$\leq$ k이다. m > k+1인 G(2$^{m}$ , 2$^{k}$ )에서 임의의 연결도-1개 이하의 노드에 고장이 있을 경우, 모든 두 노드 사이의 고장이 없는 가장 짧은 경로들의 길이의 최대값, 즉 G(2$^{m}$ , 2$^{k}$ )의 고장지름은 n이 짝수이면 di $a_{m, k}$+2 이하이고, n이 흘수이면 di $a_{m, k}$+3 이하이다. 여기서 di $a_{m, k}$는 G(2$^{m}$ , 2$^{k}$ )의 지름이다.

• Journal of KIISE:Computer Systems and Theory
• /
• v.35 no.9_10
• /
• pp.421-428
• /
• 2008

A. Ghafoor proposed Even networks as a class of fault-tolerant multiprocessor networks in [1] and analyzed so many useful properties include node disjoint paths. By introducing node disjoint paths in [1], fault diameter of Even networks is d+2(d=odd) and d+3(d=even). But the lengths of node disjoint paths proved in [1] are not the shortest. In this paper, we show that Even network Ed is node symmetric. We also propose the shortest lengths of node disjoint paths using cyclic permutation, and fault diameter of Even networks is d+1.

• Proceedings of the Korean Information Science Society Conference
• /
• 2004.10a
• /
• pp.58-60
• /
• 2004

최근에 하이퍼큐브의 망비용을 개선한 하이퍼-스타 연결망이 제안되었다. 본 논문에서는 하이퍼-스타 연결망 HS(2n, n)의 container를 이용하여 k-wide diameter가 dist(u, v)＋4이하임과 HS(2n, n)의 고장지름이 D(HS(2n, n))＋2 이하임을 보인다.

• Proceedings of the Korea Information Processing Society Conference
• /
• 2001.04a
• /
• pp.263-266
• /
• 2001

상호 연결망에서 임의의 두 노드 사이에 존재하는 노드 중복 없는 경로들의 집합을 Container라고 하는데, 본 논문에서는 계층적 하이퍼큐브 연결망의 Container가 n+1임을 보이고, 그 결과를 통하여 계층적 하이퍼큐브 연결망의 고장지름이 dia(HCN(n,n))+4 이하임을 보인다. 이러한 Container는 노드간에 메시지를 전송하는 시간을 줄일 수 있으며, 연결망의 노드 몇 개가 고장이 발생해도 통신지연시간이 발생하지 않음을 의미한다.

• Proceedings of the Korean Information Science Society Conference
• /
• 2001.04a
• /
• pp.718-720
• /
• 2001

본 논문에서는 하이퍼큐브보다 망 비용이 개선된 상호연결망 HCN(n,n)의 임의의 두 노드간에 노드중복하지 않는 n+1개의 병렬경로를 구성하는 방법을 제시하고, 그 결과를 통하여 HCN(n,n)의 고장지름이 dia(HCN(n,n))+4 이하임을 보인다. 이러한 병렬경로는 노드간에 메시지를 전송하는 시간을 줄일 수 있으며, HCN(n,n)의 노드 몇 개가 고장이 발생해도 통신지연시간이 발생하지 않음을 의미한다.