• Journal of the Institute of Electronics Engineers of Korea CI
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• v.42 no.1
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• pp.27-34
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• 2005

In this paper, we propose the Q-edge labeling method related to the graph embedding problem in binomial trees. This result is able to design a new reliable interconnection networks with maximum connectivity using Q-edge labels as jump sequence of circulant graph. The circulant graph is a generalization of Harary graph which is a solution of the optimal problem to design a maximum connectivity graph consists of n vertices End e edgies. And this topology has optimal broadcasting because of having binomial trees as spanning tree.

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.11
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• pp.1353-1362
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• 1999

그래프 드로잉이란 추상적인 그래프를 시각적으로 구성하여 2차원 평면상에 그려주는 작업으로 대칭성은 그래프 드로잉시 고려해야 하는 미적 기준들 중에서 그래프의 구조 및 특성을 표현해주는 가장 중요한 기준이다. 그러나 일반 그래프에서 대칭성을 찾아 그려 주는 문제는 NP-hard로 증명이 되어 있기 때문에 현재까지는 트리, 외부평면 그래프, 직병렬 유향 그래프나 평면 그래프 등으로 대상을 한정시켜 연구가 진행되어 왔다. 본 논문에서는 병렬 컴퓨터나 컴퓨터 네트워크 구조를 가시화 시키기 위하여 많이 사용되는 그래프인 상호연결망(interconnection network)의 대칭성을 분석하고 분석된 대칭성을 최대로 보여주는 대칭 드로잉 알고리즘을 제안하였다. 그리고 이를 기반으로 하여 상호연결망의 기존 드로잉 방법들과 본 논문에서 제안한 대칭 드로잉 등 다양한 드로잉을 지원하는 WWW 기반의 상호연결망 드로잉 시스템을 구현하였다.Abstract Graph drawing is constructing a visually-informative drawing of an abstract graph. Symmetry is one of the most important aesthetic criteria that clearly reveals the structures and the properties of graphs. However, the problem of finding geometric symmetry in general graphs is NP-hard. So the previous work has focused on the subclasses of general graphs such as trees, outerplanar graphs, series-parallel digraphs and planar graphs.In this paper, we analyze the geometric symmetry on the various interconnection networks which have many applications in the design of computer networks, parallel computer architectures and other fields of computer science. Based on these analysis, we develope algorithms for constructing the drawings of interconnection networks which show the maximal symmetries.We also design and implement Interconnection Network Drawing System (INDS) on WWW which supports the various drawings including the conventional drawings and our suggested symmetric drawings.

• Journal of information and communication convergence engineering
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• v.22 no.3
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• pp.215-220
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• 2024

This paper presents an efficient method for expanding interconnections in scenarios involving the reconstruction of interconnections across arbitrarily divided planes. Conventionally, such situations necessitate rebuilding interconnections based on all targets, ensuring minimal cost but incurring substantial time expenditure. In this paper, we present a tinkered tree algorithm designed to efficiently expand interconnections within a Euclidean plane divided into m randomly generated regions. The primary objective of this algorithm is to construct an optimal tree by utilizing the minimum spanning tree (MST) of each region, resulting in swift interconnection expansion. Interconnection construction is applied in various design fields. Notably, in the context of ad hoc networks, which lack a fixed-wired infrastructure and communicate solely with mobile hosts, the heuristic proposed in this paper is anticipated to significantly reduce costs while establishing rapid interconnections in scenarios involving expanded connection targets.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.48 no.2
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• pp.6-13
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• 2011

This paper deals with the interconnection problem in ad-hoc networks or sensor networks, where relay nodes are deployed additionally to form connections between given nodes. This problem can be reduced to a NP-hard problem. The nodes of the networks, by applications or geographic factors, can be deployed densely in some areas while sparsely in others. For such a case one can make an approximation scheme, which gives shorter execution time, for the additional node deployments by ignoring the interconnections inside the dense area of nodes. However, the case is still a NP-hard, so it is proper to establish a polynomial time approximation scheme (PTAS) by implementing a dynamic programming. The analysis can be made possible by an elaboration on making the definition of the objective function. The objective function should be defined to be able to deal with the requirement incurred by the substitution of the dense area with its abstraction.

• Journal of information and communication convergence engineering
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• v.17 no.4
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• pp.246-254
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• 2019

This paper proposes a solution to the problem of finding a subgraph for a given instance of many terminals on a Euclidean plane. The subgraph is a tree, whose nodes represent the chosen terminals from the problem instance, and whose edges are line segments that connect two corresponding terminals. The tree is required to have the maximum number of nodes while the length is limited and is not sufficient to interconnect all the given terminals. The problem is shown to be NP-hard, and therefore a genetic algorithm is designed as an efficient practical approach. The method is suitable to various probable applications in layout optimization in areas such as communication network construction, industrial construction, and a variety of machine and electronics design problems. The proposed heuristic can be used as a general-purpose practical solver to reduce industrial costs by determining feasible interconnections among many types of components over different types of physical planes.

• Proceedings of the IEEK Conference
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• 2004.06a
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• pp.167-170
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• 2004

We present a novel graph labeling problem called S-edge labeling. The constraint in this labeling is placed on the allowable edge label which is the difference between the labels of endvertices of an edge. Each edge label should be ${ a_n / a_n = 4 a_{n-l}+l,\;a_{n-1}=0}$. We show that every binomial tree is possible S-edge labeling by giving labeling schems to them. The labelings on the binomial trees are applied to their embedings into interconnection networks.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.7
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• pp.117-124
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• 1994

In this pape, we propose a graph-theoretic approach for solving the allocation problem for the synthesis of datapaths based on multiport memories. An efficient algorithm is devised by using the weighted bipartite matching algorithm to assign variables to each port of memory modules. The proposed algorithm assigns program variables into a minimum number of multiport memory modules such that usage of memory elements and interconnection cost can be kept minimal. Experimental results show that the proposed algorithm generates the datapaths with fewer registers in memory modules and less interconnection cost for several benchmarks available from the literatures.

• Journal of KIISE:Computer Systems and Theory
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• v.35 no.2
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• pp.60-65
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• 2008

The matching preclusion set of a graph is a set of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. The matching preclusion number is the minimum cardinality over all matching preclusion sets. We show in this paper that, for any $m{\geq}4$, the matching preclusion numbers of both m-dimensional restricted HL-graph and recursive circulant $G(2^m,4)$ are equal to degree m of the networks, and that every minimum matching preclusion set is the set of edges incident to a single vertex.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.471-474
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• 1998

In this paper, we consider the problem of optimal broadcasting in recursive circulants under multi-port communication model. Recursive circulant G(N, d) that is defined to be a circulant graph with N vertices and jumps of powers of d is a useful interconnection network from the viewpoint of network metrices. Our model assumes that a processor can transmit a message to $\alpha$ neighboring processors simultaneously where $\alpha$ is two or three. For the broadcasting problem, we introduce 3-trees and 4-trees. And then we show that 3-trees and 4-trees are minimum broadcast trees in 2-port model and 3-port model. Using the above results, we show that recursive circulants g(2m, 2) have optimum broadcasting time in 2-port model and 3-port model.

• Journal of information and communication convergence engineering
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• v.19 no.2
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• pp.114-119
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• 2021

This paper proposes a method to find an optimal T' with the most terminal of the subset of T' trees that can be connected by a given length by improving a memetic genetic algorithm within several constraints, when the set of terminal T is given to the Euclidean plane R². Constraint (1) is that a given length cannot connect all terminals of T, and (2) considers only the rectilinear layout of the edge connecting each terminal. The construction of interconnections has been used in various design-related areas, from network to architecture. Among these areas, there are cases where only the rectilinear layout is considered, such as wiring paths in the computer network and VLSI design, network design, and circuit connection length estimation in standard cell deployment. Therefore, the heuristics proposed in this paper are expected to provide various cost savings in the rectilinear layout.