• 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.

• 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 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.

• Structural Engineering and Mechanics
• /
• v.75 no.1
• /
• pp.71-86
• /
• 2020

This paper presents a study on the mechanical behavior of buried pipelines crossing faults using experimental and numerical methods. A self-made soil-box was used to simulate normal fault, strike-slip fault and oblique slip fault. The effects of some important parameters, including the displacement and type of fault, the buried depth and the diameter of pipe, on the deformation modes and axial strain distribution of the buried pipelines crossing faults was studied in the experiment. Furthermore, a finite element analysis (FEA) model of spring boundary was developed to investigate the performance of the buried pipelines crossing faults, and FEA results were compared with experimental results. It is found that the axial strain distribution of those buried pipelines crossing the normal fault and the oblique fault is asymmetrical along the fault plane and that of buried pipelines crossing the strike-slip fault is approximately symmetrical. Additionally, the axial peak strain appears near both sides of the fault and increases with increasing fault displacement. Moreover, the axial strain of the pipeline decreases with decreasing buried depth or increasing ratios of pipe diameter to pipe wall thickness. Compared with the normal fault and the strike-slip fault, the oblique fault is the most harmful to pipelines. Based on the accuracy of the model, the regression equations of the axial distance from the peak axial strain position of the pipeline to the fault under the effects of buried depth, pipe diameter, wall thickness and fault displacement were given.

• The Transactions of the Korea Information Processing Society
• /
• v.6 no.1
• /
• pp.75-83
• /
• 1999

recently, a new hypercube-like interconnection network, the Z-cube, was proposed. The Z-cube retains most good topological properties, however, its node degree is 3/4 of hypercube's one. Considering hardware implementations, the Z-cube is a good alternative to the hypercube. In this paper, we obtained the diameter, fault diameter and the average distance between two nodes to evaluate the communication performance of the Z-cube. The recursive structure, the shortest path between two nodes I Z-cube and recurrence relation on the average distance were deduced, and node disjoint path was introduced. Although it is generally expected that the communication performance in an interconnection network with reduced node degree falls as much as that, this paper shows that the Z-cube's diameter is the same as the hypercube's one and the average distance between two nodes in Z-cube is about 1.125 times the average distance between two nodes in the hypercube and the fault diameter of Z-cube ranges approximately from 1.4times to 1.7times the fault diameter of the hypercube.

• 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 Geotechical Society Conference
• /
• 2004.03b
• /
• pp.74-81
• /
• 2004

In this study, static end loading tests with load transfer measurement were accomplished for large diameter drilled shaft constructed in fault zone. Yield pile capacity (or ultimate pile capacity) from load-settlement curve was determined and axial load transfer behavior was measurd. The end bearing capacity was increased 2 times due to grouting the toe ground under pile base.

• Journal of the Korean Geotechnical Society
• /
• v.20 no.5
• /
• pp.135-143
• /
• 2004

In the land section of marine bridge construction site, to confirm the end bearing of large diameter drilled shaft constructed in the fault zone which was discovered unexpectedly, the hi-directional end loading tests were performed. The objectives of this study are to confirm the end bearing of the pile constructed in fault zone and the increasing effect of end bearing after grouting the base ground beneath the pile toe. After grouting the pile base ground, the settlement of pile base decreased considerably and the pile base resistance increased more than twice.

• 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.