• Proceedings of the Korean Society of Computer Information Conference
• /
• 2010.07a
• /
• pp.429-432
• /
• 2010

그래프 분할 문제는 각각의 가중치가 주어진 에지와 노드를 정해진 목적에 맞게 몇 개의 그룹으로 분할하는 문제이다. 이 문제는 휴리스틱 방법으로 해결되어져 왔으나, NP-hard 문제로 인한 지역 최적해에 빠지기 쉬운 단점을 갖는다. 유전자 알고리즘이 해결 방법으로 제시되고 있는 가운데 단순 유전자 알고리즘에서 초기의 모집단 메모리(population memory)를 이용하여 적은 크기의 모집단을 생성하고 외부메모리에 최적해들을 저장하고 있어 GA의 효율성을 높이며, 다수의 지역 최적해에 빠지지 않게 하며 수렴 속도를 향상시키는 마이크로 유전자 알고리즘을 적용한다. ${\mu}$-GA를 통해 본 논문에서는 클러스터들의 가중치를 비교적 동일하게 하는 GPP를 해결하고자 한다.

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

• IE interfaces
• /
• v.21 no.1
• /
• pp.1-7
• /
• 2008

In this paper we study the Minimum Edge Addition Problem(MEAP) to decrease the diameter of a graph. MEAP can be used for improving the serviceability of telecommunication networks with a minimum investment. MEAP is an NP-hard optimization problem. We present two mathematical programming models : One is a multi-commodity flow formulation and the other is a path partition formulation. We propose a branch-and-price algorithm to solve the path partition formulation to the optimality. We develop a polynomial time column generation sub-routine conserving the mathematical structure of a sub problem for the path partition formulation. Computational experiments show that the path partition formulation is better than the multi-commodity flow formulation. The branch-and-price algorithm can find the optimal solutions for the immediate size graphs within reasonable time.

• KIPS Transactions on Software and Data Engineering
• /
• v.7 no.5
• /
• pp.177-188
• /
• 2018

The scale of graph data has been increased rapidly because of the growth of mobile Internet applications and the proliferation of social network services. This brings upon the imminent necessity of efficient distributed and parallel graph processing approach since the size of these large-scale graphs are easily over a capacity of a single machine. Currently, there are two popular parallel graph processing approaches, vertex-centric graph processing and block centric processing. While a vertex-centric graph processing approach can easily be applied to the parallel processing system, a block-centric graph processing approach is proposed to compensate the drawbacks of the vertex-centric approach. In these systems, the initial quality of graph partition affects to the overall performance significantly. However, it is a very difficult problem to divide the graph into optimal states at the initial phase. Thus, several dynamic load balancing techniques have been studied that suggest the progressive partitioning during the graph processing time. In this paper, we present a load balancing algorithms for the block-centric graph processing approach where most of dynamic load balancing techniques are focused on vertex-centric systems. Our proposed algorithm focus on an improvement of the graph partition quality by dynamically reassigning blocks in runtime, and suggests block split strategy for escaping local optimum solution.

• 제어로봇시스템학회:학술대회논문집
• /
• 2001.10a
• /
• pp.120.3-120
• /
• 2001

We propose a new method of path planning for cleaning robots. Path planning problem for cleaning robots is different from conventional path planning problems in which finding a collision-free trajectory from a start point to a goal point is focused. In the case of cleaning robots, however, a planned path should cover all area to be cleaned. To resolve this problem in a systematic way, we propose a method based on a graph model as follows: at first, partition a given map into proper regions, then transform a divided region to a vertex and a connectivity between regions to an edge of a graph. Finally, a region is divided into sub-regions so that the graph has a unary tree which is the simplest Hamilton path. The effectiveness of the proposed method is shown by computer simulation results.

• International Journal of Computer Science & Network Security
• /
• v.22 no.9
• /
• pp.31-34
• /
• 2022

The concept of locating chromatic number of graph is a development of the concept of vertex coloring and partition dimension of graph. The locating-chromatic number of G, denoted by χ_L(G) is the smallest number such that G has a locating k-coloring. In this paper we will discussed about the procedure for determine the locating chromatic number of Origami graph using Python Programming.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.6 no.4
• /
• pp.1188-1202
• /
• 2012

In this paper, we propose a new multi-scale connected coherence tree algorithm (MCCTA) by improving the connected coherence tree algorithm (CCTA). In contrast to many multi-scale image processing algorithms, MCCTA works on multiple scales space of an image and can adaptively change the parameters to capture the coarse and fine level details. Furthermore, we design a Multi-scale Connected Coherence Tree algorithm plus Spectral graph partitioning (MCCTSGP) by combining MCCTA and Spectral graph partitioning in to a new framework. Specifically, the graph nodes are the regions produced by CCTA and the image pixels, and the weights are the affinities between nodes. Then we run a spectral graph partitioning algorithm to partition on the graph which can consider the information both from pixels and regions to improve the quality of segments for providing image segmentation. The experimental results on Berkeley image database demonstrate the accuracy of our algorithm as compared to existing popular methods.

• Proceedings of the KIEE Conference
• /
• 1988.07a
• /
• pp.557-560
• /
• 1988

In this paper, we present a new k-way partitioning algorithm for a graph of an electrical circuit wherein nodes and edges are regarded as cells (modules) and nets, respectively. In contrast to the previous work, our method is based upon a linearly ordered partition paradigm. We also claim that the maximum number of netcuts mostly governs the performance of k-way partitioning, thus having influence on the construction of a new cost function. In addition, our approach elaborates upon balancing the partition size. Our experiments show excellent results in comparison with previous k-way partitioning algorithms.

• Journal of the Korean Mathematical Society
• /
• v.45 no.6
• /
• pp.1613-1622
• /
• 2008

Let G be a graph with vertex set V(G) and edge set E(G), and let g, f be two nonnegative integer-valued functions defined on V(G) such that $g(x)\;{\leq}\;f(x)$ for every vertex x of V(G). We use $d_G(x)$ to denote the degree of a vertex x of G. A (g, f)-factor of G is a spanning subgraph F of G such that $g(x)\;{\leq}\;d_F(x)\;{\leq}\;f(x)$ for every vertex x of V(F). In particular, G is called a (g, f)-graph if G itself is a (g, f)-factor. A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {$F_1$, $F_2$, ..., $F_m$} be a factorization of G and H be a subgraph of G with mr edges. If $F_i$, $1\;{\leq}\;i\;{\leq}\;m$, has exactly r edges in common with H, we say that F is r-orthogonal to H. If for any partition {$A_1$, $A_2$, ..., $A_m$} of E(H) with $|A_i|=r$ there is a (g, f)-factorization F = {$F_1$, $F_2$, ..., $F_m$} of G such that $A_i\;{\subseteq}E(F_i)$, $1\;{\leq}\;i\;{\leq}\;m$, then we say that G has (g, f)-factorizations randomly r-orthogonal to H. In this paper it is proved that every (0, mf - (m - 1)r)-graph has (0, f)-factorizations randomly r-orthogonal to any given subgraph with mr edges if $f(x)\;{\geq}\;3r\;-\;1$ for any $x\;{\in}\;V(G)$.

• Proceedings of the Korean Society of Broadcast Engineers Conference
• /
• 2010.11a
• /
• pp.100-103
• /
• 2010

In this paper we propose a method of detecting moving object in H.264/AVC bitstream by representing the $4{\times}4$ block partition units as nodes of graph. By constructing hierarchical graph by taking into account the relation between nodes and the spatial-temporal relations between graphs in frames, we are able to track small objects, distinguish two occluded objects, and identify objects that move and stop alternatively.