• Management Science and Financial Engineering
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• 제8권1호
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• pp.1-19
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• 2002

Ordering is used to reduce the amount of fill-ins in the Cholesky factor of a symmetric positive definite matrix. One of the most efficient ordering methods is the minimum degree ordering algorithm(MDO). In this paper, we provide a few techniques that improve the performance of MDO implemented with the clique storage scheme. First, the absorption of nodes in the cliques is developed which reduces the number of cliques and the amount of storage space required for MDO. Second, we present a modified minimum degree ordering algorithm of which the number of degree updates can be reduced by introducing the lower bounds of degrees. Third, using both the lower and upper bounds of degrees, we develop an approximate minimum degree ordering algorithm. Experimental results show that the proposed algorithm is competitive with the minimum degree ordering algorithm that uses quotient graphs from the points of the ordering time and the nonzeros in the Cholesky factor.

• Kyungpook Mathematical Journal
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• 제59권4호
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• pp.591-601
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• 2019

Let ℤ_n be the ring of integers modulo n and Γ(ℤ_n) the zero-divisor graph of ℤ_n. In this paper, we study some properties of Γ(ℤ_n). More precisely, we completely characterize the diameter and the girth of Γ(ℤ_n). We also calculate the chromatic number of Γ(ℤ_n).

• 한국멀티미디어학회논문지
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• 제12권6호
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• pp.824-832
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• 2009

Multi-radio multi-channel Wireless Mesh Network requires an effective management policy to control the assignment of channels to each radio. We concentrated our investigation on modeling method and solution to find a dynamic channel assignment scheme that is adapted to change of network traffic. Multi-path routing scheme was chosen to overwhelm the unreliability of wireless link. For a particular traffic state, our optimization model found a specific traffic distribution over multi-path and a channel assignment scheme that maximizes the overall network throughput. We developed a simple heuristic method for channel assignment by gradually removing clique load to obtain higher throughput. We also presented numerical examples and discussion of our models in comparison with existing research.

• 대한수학회보
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• 제53권4호
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• pp.1197-1211
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• 2016

Let R be a finite commutative ring with nonzero identity. We define ${\Gamma}(R)$ to be the graph with vertex set R in which two distinct vertices x and y are adjacent if and only if there exists a unit element u of R such that x + uy is a unit of R. This graph provides a refinement of the unit and unitary Cayley graphs. In this paper, basic properties of ${\Gamma}(R)$ are obtained and the vertex connectivity and the edge connectivity of ${\Gamma}(R)$ are given. Finally, by a constructive way, we determine when the graph ${\Gamma}(R)$ is Hamiltonian. As a consequence, we show that ${\Gamma}(R)$ has a perfect matching if and only if ${\mid}R{\mid}$ is an even number.

• 대한수학회지
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• 제48권4호
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• pp.691-702
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• 2011

The competition graph of a digraph D is a graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x, v) and (y, v) are arcs of D. For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph. The competition number k(G) of a graph G is defined to be the smallest number of such isolated vertices. In general, it is hard to compute the competition number k(G) for a graph G and it has been one of important research problems in the study of competition graphs. In this paper, we compute the competition numbers of Hamming graphs with diameter at most three.

• 전자공학회논문지S
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• 제34S권6호
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• pp.30-37
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• 1997

We present an efficient technique, bidirectioanl inertial maximum cost search technique, for th edetection and segmentation of circular shaped objects using the spatial information around the neighborhood of the boundary candidates. This technique searches boundary candidates using local pixdl information such as pixel value and its direction. And then to exclude pseudo-boundary caused by shadows or noises, the local contrast is defined between the clique of the boundary candidates and the cliques of the background. In order to effectively segment circular shaped boundary, the technique also uses the curvature based on trigonometirc function which determines circular shaped boundary segments. Since the proposed technique is applied to the pixel cliques instead of a pixel itself, it is proposed method can easily find out circular boundaries form iamges of the PCB containing circular shaped parts and the trees with round fruits compared to boundary detection by using the pixel information and the laplacian curvature.

• 전자공학회논문지A
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• 제31A권2호
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• pp.116-124
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• 1994

This paper describes the design of a high-level synthesis system. ISyn: Interface Synthesis System for ISPS-A. which generates hardware satisfying timing constraints. The original version of ISPS is extended to be used for the description/capture of interface operations and timing constraints in the ISPS-A. To generate the schedule satisfying interface constraints the scheduling process is divided into two steps:pre-scheduling and post-scheduling. ISyn allocates hardware modules with I/O ports by the clique partitioning algorithm. Experimental results show that ISyn is capable of synthesizing hardware modules effectively for internal and/or interactive operations.

• International Journal of Knowledge Content Development & Technology
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• 제8권2호
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• pp.23-36
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• 2018

Institutional repositories (IR) are promising to be extremely advantageous to scholars especially in developing countries. IR initiatives started in India during the late nineties and the popularity of this concept is growing rapidly in the higher educational and research institutions to disseminate newly emerging knowledge and expertise. The purpose of this paper is to critically analyze the network links of IR websites among four IITs that are registered in open DOAR (Directory of Open Access Repositories) web portal. The Institutional Repositories chosen for the study are IIT Delhi, IIT Hyderabad, IIT Bombay, and IIT Kanpur. The analysis of the study focused on standard graph and network cohesion metrics, such as density, diameter, eccentricity and distances, and clustering coefficient; for an even more detailed analysis advanced centrality measures and fast algorithms such as clique census are used.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권3호
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• pp.65-75
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• 2007

A graph G is self-complementary (sc) if it is isomorphic to its complement. G is perfect if for all induced subgraphs H of G, the chromatic number of H (denoted ${\chi}$(H)) equals the number of vertices in the largest clique in H (denoted ${\omega}$(H)). An sc graph which is also perfect is known as sc perfect graph. A comparability graph is an undirected graph if it can be oriented into transitive directed graph. An sc comparability (scc) is clearly a subclass of sc perfect graph. In this paper we show that no two non-isomorphic scc graphs with n vertices each, (n<13) have same spectrum, and that the smallest positive integer for which there exists hyper-energetic scc graph is 13.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.49.3-49
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• 2001

In 1994 Adelman´s pioneer work demonstrated that deoxyribonucleic acid (DNA) could be used as a medium for computation to solve mathematical problems. He described the use of DNA based computational approach to solve the Hamiltonian Path Problem (HPP). Since then a number of combinatorial problems have been analyzed by DNA computation approaches including, for example: Maximum Independent Set (MIS), Maximal Clique and Satisfaction (SAT) Problems. In the present paper we propose a method of solving another classic combinatorial optimization problem - the eraph Coloring Problem (GCP), using specifically designed circular DNA plasmids as a computation tool. The task of the analysis is to color the graph so that no two nodes ...