• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.39-48
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• 2006

Let ${\gamma}$(G) be the domination number of a graph G. It is shown that for any $k {\ge} 0$ there exists a Cartesian graph bundle $B{\Box}_{\varphi}F$ such that ${\gamma}(B{\Box}_{\varphi}F) ={\gamma}(B){\gamma}(F)-2k$. The domination numbers of Cartesian bundles of two cycles are determined exactly when the fibre graph is a triangle or a square. A statement similar to Vizing's conjecture on strong graph bundles is shown not to be true by proving the inequality ${\gamma}(B{\bigotimes}_{\varphi}F){\le}{\gamma}(B){\gamma}(F)$ for strong graph bundles. Examples of graphs Band F with ${\gamma}(B{\bigotimes}_{\varphi}F) < {\gamma}(B){\gamma}(F)$ are given.

• Proceedings of the Korean Information Science Society Conference
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• 1998.10c
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• pp.526-528
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• 1998

영상 자료는 일반적으로 많은 정보량을 가지기 때문에 저장 공간과 전송 시간의 문제 등이 발생한다. 이 문제를 해결하기 위해 영상 압축 기법이 사용되며 그 방법 중의 하나로 벡터 양자화가 있다. 벡터 양자화는 압축률은 높지만 시간이 많이 걸리는데, 전체 처리 시간 중에서도 영상의 각 블록에 해당하는 코드벡터를 찾기 위해 주어진 코드북을 탐색하는 단계에 소요되는 시간이 가장 큰 비중을 차지한다. 본 논문에서는 코드북 탐색에 소요되는 시간을 줄여 벡터 양자화를 빠르게 하기 위한 방법으로 삼각 부등식을 이용하는 빠른 코드북 탐색법을 제안한다. 제안된 방법은 삼각 부등식을 이용해 구한 하한값을 기준으로 불필요한 계산을 줄여서 탐색 속도를 증가시킨다. 제안된 방법의 평가를 의해 100장의 256$\times$256, 256 레벨 흑백 영상을 사용하였고, 기존의 전체 탐색 방법에 비해 배 이상의 속도 향상을 얻을 수 있었다.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.569-585
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• 2022

A brief comparative survey of some generalizations of a metric space with three dimensional metric structures and different forms of the triangle inequality is done along with their topological properties. Then a common fixed point is obtained for reciprocally continuous and compatible self-maps in a G-metric space. Further, a common fixed point theorem is proved for a pair of weakly compatible self-maps on a G-metric space with the common limit range property.

• Journal of Korea Society of Industrial Information Systems
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• v.5 no.2
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• pp.16-21
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• 2000

Vector quantization(VQ) is widely used in many high-quality and high-rate data compression applications such as speech coding, audio coding, image coding and video coding. When the size of a VQ codebook is large, the computational complexity for the full codeword search method is a significant problem for many applications. A number of complexity reduction algorithms have been proposed and investigated using such properties of the codebook as the triangle inequality. This paper proposes a new fast VQ search algorithm that is based on a multi-stage structure for searching for the best codeword. Even using only two stages, a significant complexity reduction can be obtained without any loss of quality.

• Journal of Korean Institute of Industrial Engineers
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• v.26 no.4
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• pp.363-375
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• 2000

In this paper we propose a content-based image retrieval method that can search large image databases efficiently by color, texture, and shape content. Quantized RGB histograms and the dominant triple (hue, saturation, and value), which are extracted from quantized HSV joint histogram in the local image region, are used for representing global/local color information in the image. Entropy and maximum entry from co-occurrence matrices are used for texture information and edge angle histogram is used for representing shape information. Relevance feedback approach, which has coupled proposed features, is used for obtaining better retrieval accuracy. Simulation results illustrate the above method provides 77.5 percent precision rate without relevance feedback and increased precision rate using relevance feedback for overall queries. We also present a new indexing method that supports fast retrieval in large image databases. Tree structures constructed by k-means algorithm, along with the idea of triangle inequality, eliminate candidate images for similarity calculation between query image and each database image. We find that the proposed method reduces calculation up to average 92.9 percent of the images from direct comparison.