• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.335-340
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• 2019

The energy of a graph G is the sum of the absolute values of the eigenvalues of the adjacency matrix of G. Some variants of energy can also be found in the literature, in which the energy is defined for the Laplacian matrix, Distance matrix, Commonneighbourhood matrix or Seidel matrix. The Seidel matrix of the graph G is the square matrix in which $ij^{th}$ entry is -1 or 1, if the vertices $v_i$ and $v_j$ are adjacent or non-adjacent respectively, and is 0, if $v_i=v_j$. The Seidel energy of G is the sum of the absolute values of the eigenvalues of its Seidel matrix. We present here some families of pairs of graphs whose Seidel matrices have different eigenvalues, but who have the same Seidel energies.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.685-695
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• 2022

The minimum number of complete bipartite subgraphs needed to partition the edges of a graph G is denoted by b(G). A known lower bound on b(G) states that b(G) ≥ max{p(G), q(G)}, where p(G) and q(G) are the numbers of positive and negative eigenvalues of the adjacency matrix of G, respectively. When equality is attained, G is said to be eigensharp and when b(G) = max{p(G), q(G)} + 1, G is called an almost eigensharp graph. In this paper, we investigate the eigensharpness and almost eigensharpness of lexicographic products of some graphs.

• Spatial Information Research
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• v.20 no.4
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• pp.83-92
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• 2012

Location-based services (LBS) are increasingly popular due to the improvement of geo-positioning capabilities and wireless communication technology. However, in order to enjoy LBS services, a user requesting a query must send his/her exact location to the LBS provider. Therefore, it is a key challenge to preserve user's privacy while providing LBS. To solve this problem, the existing method employs a 2PASS cloaking framework that not only hides the actual user location but also reduces bandwidth consumption. However, 2PASS does not fully guarantee the actual user privacy because it does not take the real user distribution into account. Hence, in this paper, we propose a nearest neighbor query processing algorithm that supports K-anonymity property based on the weighted adjacency graph(WAG). Our algorithm not only preserves the location of a user by guaranteeing k-anonymity in a query region, but also improves a bandwidth usage by reducing unnecessary search for a query result. We demonstrate from experimental results that our algorithm outperforms the existing one in terms of query processing time and bandwidth usage.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.41 no.1
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• pp.38-46
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• 2004

Image segmentation is the task which partitions the image into meaningful regions and considered to be one of the most important steps in computer vision and image processing. Image segmentation is also widely used in object-based video compression such as MPEG-4 to extract out the object regions from the given frame. Watershed algorithm is frequently used to obtain the more accurate region boundaries. But, it is well known that the watershed algorithm is extremely sensitive to gradient noise and usually results in oversegmentation. To solve such a problem, we propose an image segmentation method which is robust to noise by using stabilized inverse diffusion equation (SIDE) and is more efficient in segmentation by employing multiresolution approach. In this paper, we apply both the region projection method using labels of adjacent regions and the region merging method based on region adjacency graph (RAG). Experimental results on noisy image show that the oversegmenation is reduced and segmentation efficiency is increased.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.10C
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• pp.1023-1032
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• 2003

Object-based coding, such as MPEG-4, enables various content-based functionalities for multimedia applications. In order to support such functionalities, as well as to improve coding efficiency, each frame of video sequences should be segmented into video objects. In this paper. we propose an effective video object segmentation method using nonlinear multiscale filtering and spatio-temporal information. Proposed method performs a spatial segmentation using a nonlinear multiscale filtering based on the stabilized inverse diffusion equation(SIDE). And, the segmented regions are merged using region adjacency graph(RAG). In this paper, we use a statistical significance test and a time-variant memory as temporal segmentation methods. By combining of extracted spatial and temporal segmentations, we can segment the video objects effectively. Proposed method is more robust to noise than the existing watershed algorithm. Experimental result shows that the proposed method improves a boundary accuracy ratio by 43% on "Akiyo" and by 29% on "Claire" than A. Neri's Method does.

• Korean Journal of Remote Sensing
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• v.22 no.6
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• pp.613-619
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• 2006

This study proposed an unsupervised image classification through the dendrogram of agglomerative clustering as a higher stage of image segmentation in image processing. The proposed algorithm is a hierarchical clustering which includes searching a set of MCSNP (Mutual Closest Spectral Neighbor Pairs) based on the data structures of RAG(Regional Adjacency Graph) defined on spectral space and Min-Heap. It also employes a multi-window system in spectral space to define the spectral adjacency. RAG is updated for the change due to merging using RNV (Regional Neighbor Vector). The proposed algorithm provides a dendrogram which is a graphical representation of data. The hierarchical relationship in clustering can be easily interpreted in the dendrogram. In this study, the proposed algorithm has been extensively evaluated using simulated images and applied to very large QuickBird imagery acquired over an area of Korean Peninsula. The results have shown it potentiality for the application of remotely-sensed imagery.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.2
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• pp.686-710
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• 2019

This work proposes a model to solve the problem of Network Coding over a one-session multicast network. The model is based on a system of restrictions that defines the packet flows received in the sink nodes as functions of the outgoing flows from the source node. A multicast network graph is used to derive a directed labeled line graph (DLLG). The successive powers of the DLLG adjacency matrix to the convergence in the null matrix permits the construction of the jump matrix Source-Sinks. In its reduced form, this shows the dependency of the incoming flows in the sink nodes as a function of the outgoing flows in the source node. The emerging packets for each outgoing link from the source node are marked with a tag that is a linear combination of variables that corresponds to powers of two. Restrictions are built based on the dependence of the outgoing and incoming flows and the packet tags as variables. The linear independence of the incoming flows to the sink nodes is mandatory. The method is novel because the solution is independent of the Galois field size where the packet contents are defined.

• The Korean Journal of Applied Statistics
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• v.33 no.2
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• pp.115-122
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• 2020

K-means clustering uses a spherical or elliptical metric to group data points; however, it does not work well for non-convex data such as the concentric circles. Spectral clustering, based on graph theory, is a generalized and robust technique to deal with non-standard type of data such as non-convex data. Results obtained by spectral clustering often outperform traditional clustering such as K-means. In this paper, we review spectral clustering and show important issues in spectral clustering such as determining the number of clusters K, estimation of scale parameter in the adjacency of two points, and the dimension reduction technique in clustering high-dimensional data.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.10C
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• pp.1363-1369
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• 2004

LDPC(Low Density Parity Check) codes are described by bipartite graphs with bit nodes and parity-check nodes. Tanner derived minimum distance bounds of the regular LDPC code in terms of the eigenvalues of the associated adjacency matrix. In this paper we generalize the Tanner's results. We derive minimum distance bounds applicable to both regular and blockwise-irregular LDPC codes. The first bound considers the relation between bit nodes in a minimum-weight codeword, and the second one considers the connectivity between parity nodes adjacent to a minimum-weight codeword. The derived bounds make it possible to describe the distance property of the code in terms of the eigenvalues of the associated matrix.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2013.10a
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• pp.773-775
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• 2013

In this paper, we consider the problem for finding a vertex sequence of the directed cycle graph from the individual neighborhood information on a reconfigurable mesh(in short, RMESH). This problem can be solved in linear time using a sequential algorithm. However, it is difficult to develop a sublinear time parallel algorithm for the problem because of its sequential nature. All kinds of polygons can be represented by directed cycles, hence a solution of the problem may be used to solving problems in which a polygon should be constructed from the adjacency information for each vertex. In this paper, we present a constant time $n{\times}n^2$ RMESH algorithm for the problem with n vertices.