• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.19 no.3
• /
• pp.193-199
• /
• 2019

In this paper I propose an algorithm of linear time complexity for NP-complete Maximum Independent Set (MIS) problem. Based on the basic property of the MIS, which forbids mutually adjoining vertices, the proposed algorithm derives the solution by repeatedly selecting vertices in the ascending order of their degree, given that the degree remains constant when vertices ${\nu}$ of the minimum degree ${\delta}(G)$ are selected and incidental edges deleted in a graph of n vertices. When applied to 22 graphs, the proposed algorithm could obtain the MIS visually yet effortlessly. The proposed linear MIS algorithm of time complexity O(n) always executes ${\alpha}(G)$ times, the cardinality of the MIS, and thus could be applied as a general algorithm to the MIS problem.

• Proceedings of the Korean Information Science Society Conference
• /
• 2012.06c
• /
• pp.314-316
• /
• 2012

대용량 지형 데이터를 실시간에 렌더링 하기 위해 여러 가지 연속상세단계 기법들이 연구되었다. 하지만 이러한 방법을 적용해도 지형 데이터가 하드웨어에서 처리할 수 있는 크기보다 클 경우 과도한 간략화로 인한 기하오차가 발생하거나 프레임률이 저하된다. 또한 기존 연속상세단계 기법을 수행하기 위해 만들어진 자료구조들 또한 지형 데이터의 크기에 비례하여 커지므로 메모리와 전처리 시간이 많이 소요된다. 본 논문에서는 적은 개수의 정점으로 효과적인 지형 렌더링이 가능한 편향맵을 다해상도로 확장하여 별도의 자료구조가 따로 필요 없는 간단한 연속상세단계 기법을 제안한다. 이 방법은 적은 메모리 용량으로 높은 정확도의 지형을 실시간에 렌더링 할 수 있다. 연속상세단계 선택은 보다 빠른 처리를 위해 GPU에서 패치 단위의 테셀레이션을 통해서 단일 패스로 수행된다. 상세단계가 선택으로 세분화 된 지형의 각 정점들은 화면 공간상의 오차를 참조하여 각각의 상세단계를 선택한 후 해당되는 편향맵에 저장된 이동벡터만큼 이동하여 최종 지형 메쉬를 생성한다. 제안한 방법은 전처리 단계를 포함한 모든 처리가 GPU에서 수행되므로 속도가 빠르고 적은 정점으로 보다 정확한 지형을 렌더링 할 수 있다.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.13 no.4
• /
• pp.107-116
• /
• 2013

This algorithm suggests a method in which a minimum spanning tree can be obtained fast by reducing the number of an algorithm execution. The suggested algorithm performs a select-and-delete process. In the select process, firstly, it performs Borůvka's first stage for all the vertices of a graph. Then it re-performs Borůvka's first stage for specific vertices and reduces the population of the edges. In the delete process, it deletes the maximum weight edge if any cycle occurs between the 3 edges of the edges with the reduced population. After, among the remaining edges, applying the valency concept, it gets rid of maximum weight edges. Finally, it eliminates the maximum weight edges if a cycle happens among the vertices with a big valency. The select-and-delete algorithm was applied to 9 various graphs and was evaluated its applicability. The suggested select process is believed to be the vest way to choose the edges, since it showed that it chose less number of big edges from 6 graphs, and only from 3 graphs, comparing to the number of edges that is to be performed when using MST algorithm. When applied the delete process to Kruskal algorithm, the number of performances by Kruskal was less in 6 graphs, but 1 more in each 3 graph. Also, when using the suggested delete process, 1 graph performed only the 1st stage, 5 graphs till 2nd stage, and the remaining till 3rd stage. Finally, the select-and-delete algorithm showed its least number of performances among the MST algorithms.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.22 no.5
• /
• pp.1-6
• /
• 2022

This paper deals with the maximum cardinality matching(MCM) problem. The augmenting path technique is well known in MCM. MCM is obtained by $O({\sqrt{n}}m)$ time complexity augmenting path algorithm for the general graph, and O(m log n) algorithm for the bipartite graph. On the other hand, this paper suggests O(n) linear time algorithm. The proposed algorithm based on the basic principle of as possible as largest selected inter-vertex edges in order to obtain the MCM. This paper simply selects edge {u,𝜐} that the minimum degree vertex u and minimum degree vertex 𝜐 in N_G(u) 𝜈(G)=k times iteration. For various general and bipartite graphs experimental data, this algorithm can be get the 𝜈(G) exactly.

• Journal of KIISE:Computer Systems and Theory
• /
• v.26 no.8
• /
• pp.863-874
• /
• 1999

세분화란 초기 원형 모델의 삼각형 메쉬를 여러 개의 작은 메쉬로 변환하는 기법으로, 간략화 된 모델을 다시 원상태로 표현하기 위해 사용된다. 기존의 보간에 의한 세분화는 전체 모델의 에지에 일률적으로 세분화를 적용하기 때문에, 효과가 적은 부분까지도 세분화가 수행하게 되어 효율이 떨어진다. 본 논문에서는 정점 변화율을 기반으로 에지를 선택하여 세분화를 수행한다. 따라서 원형 메쉬를 변환하여 세분화된 메쉬를 생성할 때, 모델의 각 부분들은 정점 변화율의 차이에 의해 서로 다른 세분화 정도를 가지게 된다. 이 과정을 통해 원형 모델의 곡률 특성이 반영된 세분화를 수행할 수 있게 되고, 전체 모델의 세분화 정도를 조정하는 것도 가능해진다. Abstract The subdivision is a mesh transformation, which makes an original triangle mesh to subdivided meshes. This method is used for recovering original model from simplified model. The existing subdivision based on interpolation is inefficient, because it is targeted for whole edges of mesh model. Therefore, this method applies to non-effective parts. In this paper the subdivision is executed by edge selection based on curvature. When original model is transformed to subdivided model by proposed method, the parts of model has different subdivision degrees by means of the averages of vertex curvature.Proposed method makes it enable subdivision, which deploy characteristics of curvatures of original model and adjusting a degree of subdivision in whole model.

• Journal of Broadcast Engineering
• /
• v.10 no.4 s.29
• /
• pp.632-642
• /
• 2005

This paper presents a new vertex selection scheme for the polygon-based contour approximation. In the proposed method, the entire contour is partitioned into partial segments and they are approximated adaptively with variable accuracy. The approximation accuracy of each segment is controlled based on its relative significance. By computing the relative significance with the texture degradation in the approximation error region, the visual quality enhancement in the reconstructed frames can be achieved under the same amount of the contour data. For this purpose, a decision rule for $d_{max}$ is derived based on inter-region contrasts. In addition, an adaptive vertex selection method using the derived rule is proposed. Experimental results are presented to show the superiority of the proposed method over conventional methods.

• Journal of the Korea Society of Computer and Information
• /
• v.16 no.7
• /
• pp.85-93
• /
• 2011

The Vertex Coloring Problem hasn't been solved in polynomial time, so this problem has been known as NP-complete. This paper suggests linear time algorithm for Vertex Coloring Problem (VCP). The proposed algorithm is based on assumption that we can't know a priori the minimum chromatic number ${\chi}(G)$=k for graph G=(V,E) This algorithm divides Vertices V of graph into two parts as independent sets $\overline{C}$ and cover set C, then assigns the color to $\overline{C}$. The element of independent sets $\overline{C}$ is a vertex ${\upsilon}$ that has minimum degree ${\delta}(G)$ and the elements of cover set C are the vertices ${\upsilon}$ that is adjacent to ${\upsilon}$. The reduced graph is divided into independent sets $\overline{C}$ and cover set C again until no edge is in a cover set C. As a result of experiments, this algorithm finds the ${\chi}(G)$=k perfectly for 26 Graphs that shows the number of selecting ${\upsilon}$ is less than the number of vertices n.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.24 no.10B
• /
• pp.1937-1945
• /
• 1999

In paper, we propose a 3D polygonal mesh simplification technique based on vertex clustering. The proposed method differentiates the size of each cluster according to the local property of a 3D object. We determine the size of clusters by considering the normal vector of triangles and the vertex distribution. The subdivisions of cluster are represented by octree. In this paper, we use the Harsdorff distance between the original mesh and the simplified one as a meaningful error value. Because proposed method adaptively determine the size of cluster according to the local property of the mesh, it has smaller error as compared with the previous methods and represent the small regions on detail. Also it can generate a multiresolution model and selectively refine the local regions.

• Journal of the Korea Society of Computer and Information
• /
• v.19 no.7
• /
• pp.103-111
• /
• 2014

This paper proposes a modified algorithm that improves on Dijkstra's algorithm by applying it to purely two-way traffic paths, given that a road where bi-directional traffic is made possible shall be considered as an undirected graph. Dijkstra's algorithm is the most generally utilized form of shortest-path search mechanism in GPS navigation system. However, it requires a large amount of memory for execution for it selects the shortest path by calculating distance between the starting node and every other node in a given directed graph. Dijkstra's algorithm, therefore, may occasionally fail to provide real-time information on the shortest path. To rectify the aforementioned shortcomings of Dijkstra's algorithm, the proposed algorithm creates conditions favorable to the undirected graph. It firstly selects the shortest path from all path vertices except for the starting and destination vertices. It later chooses all vertex-outgoing edges that coincide with the shortest path setting edges so as to simultaneously explore various vertices. When tested on 9 different undirected graphs, the proposed algorithm has not only successfully found the shortest path in all, but did so by reducing the time by 60% and requiring less memory.

• Journal of the Korea Society of Computer and Information
• /
• v.20 no.1
• /
• pp.227-235
• /
• 2015

In this paper, I propose a linear time algorithm devised to produce exact solution to NP-complete maximum clique problem. The proposed algorithm firstly, from a given graph G=(V,E), sets vertex $v_i$ of the maximum degree ${\Delta}(G)$ as clique's major vertex. It then selects vertex $v_j$ of ${\Delta}(G)$ among vertices $N_G(v_i)$ that are adjacent to $v_i$, only to determine $N_G(v_i){\cap}N_G(v_j)$ as candidate cliques w and $v_k$. Next it obtains $w=w{\cap}N_G(v_k)$ by sorting $d_G(v_k)$ in the descending order. Lastly, the algorithm executes the same procedure on $G{\backslash}w$ graph to compare newly attained cliques to previously attained cliques so as to choose the lower. With this simple method, multiple independent cliques would also be attainable. When applied to various regular and irregular graphs, the algorithm proposed in this paper has obtained exact solutions to all the given graphs linear time O(n).