• ETRI Journal
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• v.43 no.1
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• pp.64-73
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• 2021

Two-dimensional torus network nodes are typically interconnected using XY routing algorithm for transmitting a packet from a source node to a destination node. In XY routing, if all the paths are used efficiently, the throughput and latency can be improved. In this paper, to utilize all the paths efficiently, we propose a novel binary optical routing algorithm (BORA) to improve the throughput and latency. The throughput is calculated according to the injection rate and number of packets received at the destination. The XY routing algorithm and proposed BORA are implemented using objective modular network testbed in C++ simulation software and the results are analyzed and compared. In this paper, the simulation results show that the network latency reduces to 50% while using the proposed algorithm; moreover, the throughput is also improved.

• ETRI Journal
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• v.29 no.3
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• pp.405-407
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• 2007

A globally adaptive load-balanced routing algorithm for torus interconnection networks is proposed. Unlike previously published algorithms, this algorithm employs a new scheme based on collision detection to handle deadlock, and has higher routing adaptability than previous algorithms. Simulation results show that our algorithm outperforms previous algorithms by 16% on benign traffic patterns, and by 10% to 21% on adversarial traffic patterns.

• Journal of Korea Multimedia Society
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• v.13 no.8
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• pp.1183-1193
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• 2010

The pyramid graph is well known in parallel processing as a interconnection network topology based on regular square mesh and tree architectures. The enhanced pyramid graph is an alternative architecture by exchanging mesh into the corresponding torus on the base for upgrading performance than the pyramid. In this paper, we adopt a strategy of classification into two disjoint groups of edges in regular square torus as a basic sub-graph constituting of each layer in the enhanced pyramid graph. Edge set in the torus graph is considered as two disjoint sub-sets called NPC(represents candidate edge for neighbor-parent) and SPC(represents candidate edge for shared-parent) whether the parents vertices adjacent to two end vertices of the corresponding edge have a relation of neighbor or sharing in the upper layer of the enhanced pyramid graph. In addition, we also introduce a notion of shrink graph to focus only on the NPC-edges by hiding SPC-edges within the shrunk super-vertex on the resulting shrink graph. In this paper, we analyze that the lower and upper bounds on the number of NPC-edges in a Hamiltonian cycle constructed on $2^n{\times}2^n$ torus is $2^{2n-2}$ and $3{\cdot}2^{2n-2}$ respectively. By expanding this result into the enhanced pyramid graph, we also prove that the maximum number of NPC-edges containable in a Hamiltonian cycle is $4^{n-1}$-2n+1 in the n-dimensional enhanced pyramid.

• Journal of KIISE:Computer Systems and Theory
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• v.35 no.8
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• pp.361-371
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• 2008

In this paper, the hypercube, hyperpetersen networks, whose degree is increasing in accordance with expansion of number of node and complete binary tree are one-to-one embedded into peterson-torus(PT) network which has fixed degree. The one-to-one embedding has less risk of overload or idle for the processor comparative to one-to-many and many-to-one embedding. For the algorithms which were developed on hypercube or hyperpetersen are used for PT network, it is one-to one embedded at expansion ${\doteqdot}1$, dilation 1.5n+2 and link congestion O(n) not to generate large numbers of idle processor. The complete binary tree is embedded into PT network with link congestion =1, expansion ${\doteqdot}5$ and dilation O(n) to avoid the bottleneck at the wormhole routing system which is not affected by the path length.

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

• Journal of KIISE:Computer Systems and Theory
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• v.27 no.3
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• pp.287-299
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• 2000

In this paper, we classify multicast methods into three categories, i.e., tree-based, path-based, and hybrid-based multicasts, for a multicomputer employing the bidirectional torus network and wormhole routing. We propose the dynamic partition multicast routing (DPMR) as a path-based algorithm. As a hybrid-based algorithm, we suggest the hybrid multicast routing (HMR), which employs the tree-based approach in the first phase of routing and the path-based approach in the second phase. Performance is measured in terms of the average latency for various message length to compare three multicast routing algorithms. We also compare the performance of wormhole routing having variable buffer size with virtual cut-through switching. The message latency for each switching method is compared using the DPMR algorithm to evaluate the buffer size trade-off on the performance.

• The KIPS Transactions:PartA
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• v.8A no.2
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• pp.147-156
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• 2001

A high performance routing switch is an essential device to either the high performance parallel processing or communication networks that handle multimedia transfer systems such as VOD. The high performance routing chip called STC104 is a typical example in the technical aspect which has 32 bidirectional links of 100Mbps transfer sped. It has exploited new technologies, such as wormhole routing, interval labeling, and adaptive routing method. The high speed router has been applied into some parallel processing system as a single chip. However, its performance over the various interconnection networks with multiple routing chips has not been studied. In this paper, the strucrtures and characteristics of the STC104 have been investigated in order to evaluate the high speed router. Various topology of the STC104, such as meshes, torus, and N-cube are defined and constructed. Algorithms of packet transmission have been proposed based on the interval labeling and the group adaptive routing method implemented in the interconnected network. Multicast algorithms, which are often requited to the processor networks and broadcasting systems, modified from U-mesh and U-torus algorithms have also been proposed overcoming the problems of point-to-point communication.

• Journal of Korea Multimedia Society
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• v.11 no.9
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• pp.1227-1237
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• 2008

In this paper, we analyze topological properties and embedding of Folded Hyper-Star network to further improve the network cost of Hypercube, a major interconnection network. Folded Hyper-Star network has a recursive expansion and maximal fault tolerance. The result of embedding is that Folded Hypercube $FQ_n$ and $n{\times}n$ Torus can be embedded into Folded Hyper-Star FHS(2n,n) with dilation 2. Also, we show Folded Hyper-Star FHS(2n,n) can be embedded into Folded Hypercube $FQ_{2n-1}$ with dilation 1.

• The KIPS Transactions:PartA
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• v.16A no.6
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• pp.501-508
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• 2009

In this paper, we prove that folded hyper-star network FHS(2n,n) is node-symmetric and a bipartite network. We show that FHS(2n,n) can be embedded into odd network On+1 with dilation 2, congestion 1 and Od can be embedded into FHS(2n,n) with dilation 2 and congestion 1. Also, we show that $2n{\time}n$ torus can be embedded into FHS(2n,n) with dilation 2 and congestion 2.

• The Transactions of the Korea Information Processing Society
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• v.5 no.10
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• pp.2615-2626
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• 1998

In this paper, we propose a new interconnection network called RFM graph, whichis the merger of the directed rotator and Faber-Moore graph, and analyze fault tolerance, routing algorithm node disjoint cycles and broadcasting algorithm. We also describe methods to embed star graph, 2 dimesional torus and bubblesort graph into RFM graph with unit expasion and dilation 2.