• The KIPS Transactions:PartA
• /
• v.18A no.5
• /
• pp.205-214
• /
• 2011

We propose a new interconnection network, called Twisted cube torus(TT) network based on well-known 3-dimensional twisted cube. Twisted cube torus network has smaller diameter and improved network cost than honeycomb torus with the same number of nodes. In this paper, we propose routing algorithm of Twisted cube torus network and analyze its diameter, network cost, bisection width and hamiltonian cycle.

• Journal of KIISE:Computer Systems and Theory
• /
• v.32 no.5
• /
• pp.196-208
• /
• 2005

In multiprocessor systems, interconnection network design is critical for overall system performance. Popular interconnection networks, which are generally considered, are meshes, rings, and hierarchical rings. In this paper, we propose (')Torus Ring('), which is a modified version of hierarchical ring. Torus Ring has the same complexity as the hierarchical rings, but the only difference is the way it connects the local rings. It has an advantage over the hierarchical rings when the destination of a packet is the neighbor local ring in the reverse direction. Though the average number of hops in Torus Ring is equal to that of the hierarchical rings when assuming the uniform distribution of each transaction, the benefits of the number of hops are expected to be larger because of the spatial locality in the real environment of parallel programming. In the simulation results, latencies in the interconnection network are reduced by up to 19$\%$, and the execution times are reduced by up to 10$\%$.

• Journal of KIISE:Computer Systems and Theory
• /
• v.35 no.6
• /
• pp.263-272
• /
• 2008

We propose and analyze a new interconnection network, called petersen-torus(PT) network based on well-known petersen graph. PT network has a smaller diameter and a smaller network cost than honeycomb torus with same number of nodes. In this paper, we propose optimal routing algorithm and hamiltonian cycle algorithm. We derive diameter, network cost and bisection width.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.18 no.5
• /
• pp.1116-1121
• /
• 2014

Mesh structure is one of typical interconnection networks, and it is used in the part of VLSI circuit design. Torus and Hyper-Torus are advanced interconnection networks in the part of diameter and fault-tolerance of mesh structure. In this paper, we will analyze embedding between Torus and Hyper-Torus networks. We will show T(4k,2l) can be embedded into QT(m,n) with dilation 5, congestion 4, expansion 1. And QT(m,n) can be embedded into T(4k,2l) with dilation 3, congestion 3, expansion 1.

• Journal of KIISE:Computer Systems and Theory
• /
• v.36 no.3
• /
• pp.158-170
• /
• 2009

In this paper, we propose the new torus network which has the hypercube Q3 as the basic module. The proposed Hyper-torus has the degree 4, and is the network which has the scalability, and the fine diameter. If we compare the class of the torus in the viewpoint of network cost, the hyper-torus with $1.4{\sqrt{N}}$+ 16 is proved to be approximately 65% than the torus with $4{\sqrt{N}}$ and 50% than the honeycomb with $2.45{\sqrt{N}}$. This result means that hyper-torus is better for the class of the existing mesh in the viewpoint of network cost.

• The KIPS Transactions:PartA
• /
• v.15A no.4
• /
• pp.189-198
• /
• 2008

In this paper, we prove mesh-like networks can be embedded into Petersen-Torus(PT) networks. Once interconnection network G is embedded in H, the parallel algorithm designed in Gcan be applied to interconnection network H. The torus is embedded into PT with dilation 5, link congestion 5 and expansion 1 using one-to-one embedding. The honeycomb mesh is embedded into PT with dilation 5, link congestion 2 and expansion 5/3 using one-to-one embedding. Additional, We derive average dilation. The embedding algorithm could be available in both wormhole routing system and store-and-forward routing system by embedding the generally known Torus and honeycomb mesh networks into PT at 5 or less of dilation and congestion, and the processor throughput could be minimized at simulation through one-to-one.

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

• ETRI Journal
• /
• v.31 no.3
• /
• pp.327-329
• /
• 2009

In a network, broadcasting is the dissemination of a message from a source node holding a message to all the remaining nodes through a call. This letter proposes a one-to-all broadcasting algorithm in the Petersen-torus network PT(n, n) for the single-link-available and multiple-link-available models. A PT(n, n) is a regular network whose degree is 4 and number of nodes is $10n^2$, where the Petersen graph is set as a basic module, and the basic module is connected in the form of a torus. A broadcasting algorithm is developed using a divide-and-conquer technique, and the time complexity of the proposed algorithm approximates n+4, the diameter of PT(n, n), which is the lower bound of the time complexity of broadcasting.

• Journal of the Korea Society for Simulation
• /
• v.6 no.2
• /
• pp.89-104
• /
• 1997

Performance bottleneck of parallel computer systems has mostly been I/O devices because of disparity between processor speed and I/O speed. Therefore I/O node placement strategy is required such that it can minimize the number of I/O nodes, I/O access time and I/O traffic in an interconnection network. In this paper, we propose an optimal distance-k embedding algorithm, and analyze its effect on system performance when this algorithm is applied to n x n torus architecture. We prove this algorithm is an efficient I/O node placement using software simulation. I/O node placement using the proposed algorithm shows the highest performance among other I/O node placements in all cases. It is because locations of I/O nodes are uniformly distributed in the whole network, resulting in reduced traffic in the intE'rconnection network.

• 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.