Hyeong-Ok Lee

Hyper-Star Graph: A New Interconnection Network Improving the Network Cost of the Hypercube

In this paper, we introduce the hyper-star graph HS(n, k) as a new interconnection network, and discuss its properties such as faulttolerance, scalability, isomorphism, routing algorithm, and diameter. A hyper-star graph has merits when degree × diameter is used as a desirable quality measure of an interconnection network because it has a small degree and diameter. We also introduce a variation of HS(2k, k), folded hyper-star graphs FHS(2k, k) to further improve the cost degree × diameter of a hypercube: when FHS(2k, k) and an n-dimensional hypercube have the same number of nodes, degree × diameter of FHS(2k, k) is less than (k +1)(⌈logK⌉+1) whereas a hypercube is n2, where K = 2k/ k). It shows that FHS(2k, k) is superior to a hypercube and its variations in terms of the cost, degree × diameter.

Embedding hypercubes, rings, and odd graphs into hyper-stars

Hypercubes and star graphs are two of the most fundamental classes of interconnection networks. The class of hyper-stars was introduced as a hybrid of these two classes. In this note, we establish topological relationship between the hyper-stars and three known classes of networks, namely, hypercubes, tori and odd graphs, via embedding.

Independent spanning trees on even networks

The use of multiple independent spanning trees (ISTs) for data broadcasting in networks provides a number of advantages, including the increase of fault-tolerance and bandwidth. Thus, the designs of multiple ISTs on several classes of networks have been widely investigated. In this paper, we give an algorithm to construct ISTs on even networks, and show that these ISTs are optimal for height and path lengths, and each path in the ISTs has length at most the length of the shortest path+4 in the even network.

Topological and Communication Aspects of Hyper-Star Graphs

A hyper-star graph HS(m,k) has been introduced as a class of lower cost interconnection networks. Hyper-star graph has more merit than hypercube when degree × diameter is used as a cost measure. In other words, they have smaller degree and diameter than hypercubes. In this paper, we consider some of the important properties of hyper-star graphs such as symmetry, w-diameter, and fault diameter. We show that HS(2n,n) is node-symmetric. We also show that the w-diameter of HS(2n,n) is bounded by the shortest path length plus 4, and fault diameter of HS(2n,n) is bounded by its diameter plus 2. In addition, we introduce an efficient broadcasting scheme in hyper-star graphs based on a spanning tree with minimum height.

Petersen-Torus Networks for Multicomputer Systems

In this paper, we propose and analyze a new interconnection network, called Petersen-torus (PT) network based on well-known Petersen graph. Petersen graph is the graph with the most desirable network cost to the number of nodes, such that it has the most number of nodes as 10 among graphs having degree 3 and diameter 2. Taking advantage of Petersen graph, PT was designed in place of Petersen graph having 10 nodes per node of torus. PT network has a smaller diameter and a smaller network cost than honeycomb torus with same nodes. We propose routing algorithm and we derive diameter, network cost and bisection width.

Matrix-Star graphs: a new interconnection network based on matrix operations

In this paper, we introduce new interconnection networks matrix-star graphsMTSn1,...,nk where a node is represented by n1 × ... × nk matrix and an edge is defined by using matrix operations. A matrix-star graph MTS2,n can be viewed as a generalization of the well-known star graph such as degree, connectivity, scalability, routing, diameter, and broadcasting. Next, we generalize MTS2,n to 2-dimensional and 3-dimensional matrix-star graphs MTSk, n, MTSk, n,p. One of important desirable properties of interconnection networks is network cost which is defined by degree times diameter. The star graph, which is one of popular interconnection topologies, has smaller network cost than other networks. Recently introduced network, the macro-star graph has smaller network cost than the star graph. We further improve network cost of the macro-star graph: Comparing a matrix-star graph

Analysis of the Adoption Status of Cloud Computing by Country

MTS_{k,k,k}(k = \sqrt[3]{n^{2}})

Comments on “A Class of Fault-Tolerant Multiprocessor Networks”

with n2! nodes to a macro-star graph MS(n–1,n–1) with ((n–1)2+1)! nodes, network cost of MTSk,k, k is O(n2.7) and that of MS(n–1,n–1) is O(n3). It means that a matrix-star graph is better than a star graph and a macro-star graph in terms of network cost.

Comments on "A Study of Odd Graphs as Fault-Tolerant Interconnection Networks"

Cloud computing is a major area of interest in information technology (IT), which offers the possibility of green IT implementation by reducing operating costs and carbon emissions. Other advantages of cloud computing include scalability, flexibility, reliability, and high performance. Many countries, such as the USA, UK, Japan, and Germany, have introduced and used cloud computing to their IT infrastructure. However, the adoption of cloud computing in South Korea is still in the early stages compared to such countries. This paper presents an analysis of the current adoption status of cloud computing in the USA, UK, and South Korea to seek some directions for the introduction of cloud computing technologies in Korean government agencies and public institutions.

Embedding algorithms for star, bubble-sort, rotator-faber-moore, and pancake graphs

A. Ghafoor presented node-disjoint paths of even networks using Figs. 4, 5, 6,and 7 (Ghafoor, IEEE Trans. Reliability, vol. 38, no. 1, pp. 5-15). However, the paper contains errors which cause confusion. We show that the node-disjoint paths, and Theorem 4 (Ghafoor, IEEE Trans. Reliability, vol. 38, no. 1, pp. 5-15), are not correct. We propose advanced node-disjoint paths, and prove that the fault diameter of even networks is d+1. This is optimal.