• 제어로봇시스템학회논문지
• /
• 제18권7호
• /
• pp.617-621
• /
• 2012

This paper studies asymptotic consensus problem for linear multi-agent systems. We propose a distributed state feedback control algorithm for solving the problem under fixed and undirected network communication. In contrast with the conventional algorithms that use global information (e.g., graph connectivity), the proposed algorithm only uses local information from neighbors. The principle for achieving asymptotic consensus is that, for each agent, a distributed update law gradually increases the coupling gain of LQR-type feedback and thus, the overall stability of the multi-agent system is recovered by the gain margin of LQR.

• 제어로봇시스템학회논문지
• /
• 제20권5호
• /
• pp.526-532
• /
• 2014

In this paper, we present and analyze a LQ (Linear Quadratic) inverse optimal state-consensus protocol for continuous-time multi-agent systems with undirected graph topology. By Lyapunov analysis of the state-consensus error dynamics, we show the sufficient conditions on the algebraic connectivity of the graph to guarantee LQ inverse optimality and closed-loop stability. A more relaxed stability condition is also provided in terms of the algebraic connectivity. Finally, a formation control protocol for multiple mobile robots is proposed based on the target LQ inverse optimal consensus protocol, and the simulation results are provided to verify the performance of the proposed LQ inverse formation control method.

• Journal of Electrical Engineering and Technology
• /
• 제3권3호
• /
• pp.436-443
• /
• 2008

This paper presents a new method for building detection and reconstruction from aerial images. In our approach, we extract useful building location information from the generated disparity map to segment the interested objects and consequently reduce unnecessary line segments extracted in the low level feature extraction step. Hypothesis selection is carried out by using an undirected graph, in which close cycles represent complete rooftops hypotheses. We test the proposed method with the synthetic images generated from Avenches dataset of Ascona aerial images. The experiment result shows that the extracted 3D line segments of the reconstructed buildings have an average error of 1.69m and our method can be efficiently used for the task of building detection and reconstruction from aerial images.

• Kyungpook Mathematical Journal
• /
• 제61권3호
• /
• pp.661-669
• /
• 2021

For a simple, undirected graph G = (V, E), a perfect Roman dominating function (PRDF) f : V → {0, 1, 2} has the property that, every vertex u with f(u) = 0 is adjacent to exactly one vertex v for which f(v) = 2. The weight of a PRDF is the sum f(V) = ∑_v∈V f(v). The minimum weight of a PRDF is called the perfect Roman domination number, denoted by γ_R^P(G). Given a graph G and a positive integer k, the PRDF problem is to check whether G has a perfect Roman dominating function of weight at most k. In this paper, we first investigate the complexity of PRDF problem for some subclasses of bipartite graphs namely, star convex bipartite graphs and comb convex bipartite graphs. Then we show that PRDF problem is linear time solvable for bounded tree-width graphs, chain graphs and threshold graphs, a subclass of split graphs.

• Kyungpook Mathematical Journal
• /
• 제62권1호
• /
• pp.193-204
• /
• 2022

A subset S of V(G), where G is a simple undirected graph, is a hop dominating set if for each v ∈ V(G)＼S, there exists w ∈ S such that d_G(v, w) = 2 and it is a locating-hop set if N_G(v, 2) ∩ S ≠ N_G(v, 2) ∩ S for any two distinct vertices u, v ∈ V(G)＼S. A set S ⊆ V(G) is a locating-hop dominating set if it is both a locating-hop and a hop dominating set of G. The minimum cardinality of a locating-hop dominating set of G, denoted by 𝛄_lh(G), is called the locating-hop domination number of G. In this paper, we investigate some properties of this newly defined parameter. In particular, we characterize the locating-hop dominating sets in graphs under some binary operations.

• 한국경영과학회지
• /
• 제33권3호
• /
• pp.17-28
• /
• 2008

The Steiner arborescence problem is known to be NP-hard. The objective of this problem is to find a minimal Steiner tree which starts from a designated node and spans all given terminal nodes. This paper proposes a method based on a two-step procedure to solve this problem efficiently. In the first step, graph reduction rules eliminate useless nodes and arcs which do not contribute to make an optimal solution. In the second step. ant colony algorithm with use of Prim's algorithm is used to solve the Steiner arborescence problem in the reduced graph. The proposed method based on a two-step procedure is tested in the five test problems. The results show that this method finds the optimal solutions to the tested problems within 50 seconds. The algorithm can be applied to undirected Steiner tree problems with minor changes. 18 problems taken from Beasley are used to compare the performances of the proposed algorithm and Singh et al.'s algorithm. The results show that the proposed algorithm generates better solutions than the algorithm compared.

• 디지털융복합연구
• /
• 제20권2호
• /
• pp.345-351
• /
• 2022

단순 무방향 그래프 G 의 L(2,1)-coloring은 d(u,v)가 두 정점 사이의 거리일 때 두 가지 조건 (1) d(x,y) = 1 라면 |f(x)-f(y)|≥ 2, (2) d(x,y) = 2 라면 |f(x)-f(y)|≥ 1 을 만족하는 함수 f : V → [0,1,…,k]를 정의하는 것이다. 임의의 L(2,1)-coloring c 에 대하여 G 의 c-span 은 λ(c)=max{|c(u)-c(v)|| u,v∈V} 이며, L(2,1)-coloring number 인 λ(G)는 모든 가능한 c 에 대하여 λ(G) = min{λ(c)} 로 정의된다. 본 논문에서는 Harary의 정리에 기반하여 지름이 2인 그래프에 대하여 여그래프에 해밀턴 경로의 존재여부를 Tabu Search를 사용해 판단하고 이를 통해 λ(G)가 n(=|V|)과 같음을 분석한다.

• 한국생물정보학회:학술대회논문집
• /
• 한국생물정보시스템생물학회 2005년도 BIOINFO 2005
• /
• pp.267-271
• /
• 2005

The goal of data mining is to extract new and useful knowledge from large scale datasets. As the amount of available data grows explosively, it became vitally important to develop faster data mining algorithms for various types of data. Recently, an interest in developing data mining algorithms that operate on graphs has been increased. Especially, mining frequent patterns from structured data such as graphs has been concerned by many research groups. A graph is a highly adaptable representation scheme that used in many domains including chemistry, bioinformatics and physics. For example, the chemical structure of a given substance can be modelled by an undirected labelled graph in which each node corresponds to an atom and each edge corresponds to a chemical bond between atoms. Internet can also be modelled as a directed graph in which each node corresponds to an web site and each edge corresponds to a hypertext link between web sites. Notably in bioinformatics area, various kinds of newly discovered data such as gene regulation networks or protein interaction networks could be modelled as graphs. There have been a number of attempts to find useful knowledge from these graph structured data. One of the most powerful analysis tool for graph structured data is frequent subgraph analysis. Recurring patterns in graph data can provide incomparable insights into that graph data. However, to find recurring subgraphs is extremely expensive in computational side. At the core of the problem, there are two computationally challenging problems. 1) Subgraph isomorphism and 2) Enumeration of subgraphs. Problems related to the former are subgraph isomorphism problem (Is graph A contains graph B?) and graph isomorphism problem(Are two graphs A and B the same or not?). Even these simplified versions of the subgraph mining problem are known to be NP-complete or Polymorphism-complete and no polynomial time algorithm has been existed so far. The later is also a difficult problem. We should generate all of 2$^n$ subgraphs if there is no constraint where n is the number of vertices of the input graph. In order to find frequent subgraphs from larger graph database, it is essential to give appropriate constraint to the subgraphs to find. Most of the current approaches are focus on the frequencies of a subgraph: the higher the frequency of a graph is, the more attentions should be given to that graph. Recently, several algorithms which use level by level approaches to find frequent subgraphs have been developed. Some of the recently emerging applications suggest that other constraints such as connectivity also could be useful in mining subgraphs : more strongly connected parts of a graph are more informative. If we restrict the set of subgraphs to mine to more strongly connected parts, its computational complexity could be decreased significantly. In this paper, we present an efficient algorithm to mine frequent subgraphs that are more strongly connected. Experimental study shows that the algorithm is scaling to larger graphs which have more than ten thousand vertices.

• Kyungpook Mathematical Journal
• /
• 제62권3호
• /
• pp.437-453
• /
• 2022

Unlike for polynomial rings, the notion of multiplication for the near-ring of polynomials is the substitution operation. This leads to somewhat surprising results. Let S be an abelian left near-ring with identity. The relation ~ on S defined by letting a ~ b if and only if ann_S(a) = ann_S(b), is an equivalence relation. The compressed zero-divisor graph 𝚪_E(S) of S is the undirected graph whose vertices are the equivalence classes induced by ~ on S other than [0]_S and [1]_S, in which two distinct vertices [a]_S and [b]_S are adjacent if and only if ab = 0 or ba = 0. In this paper, we are interested in studying the compressed zero-divisor graphs of the zero-symmetric near-ring of polynomials R₀[x] and the near-ring of the power series R₀[[x]] over a commutative ring R. Also, we give a complete characterization of the diameter of these two graphs. It is natural to try to find the relationship between diam(𝚪_E(R₀[x])) and diam(𝚪_E(R₀[[x]])). As a corollary, it is shown that for a reduced ring R, diam(𝚪_E(R)) ≤ diam(𝚪_E(R₀[x])) ≤ diam(𝚪_E(R₀[[x]])).

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제9권1호
• /
• pp.358-377
• /
• 2015

In this paper, we propose a novel approach for trajectory recovery. Our system uses a triangulation procedure for skeletonization and graph theory to extract the trajectory. Skeletonization extracts the polyline skeleton according to the polygonal contours of the handwritten characters, and as a result, the junction becomes clear and the characters that are touching each other are separated. The approach for the trajectory recovery is based on graph theory to find the optimal path in the graph that has the best representation of the trajectory. An undirected graph model consisting of one or more strokes is constructed from a polyline skeleton. By using the polyline skeleton, our approach accelerates the process to search for an optimal path. In order to evaluate the performance, we built our own dataset, which includes testing and ground-truth. The dataset consist of thousands of handwritten characters and word images, which are extracted from five handwritten documents. To show the relative advantage of our skeletonization method, we first compare the results against those from Zhang-Suen, a state-of-the-art skeletonization method. For the trajectory recovery, we conduct a comparison using the Root Means Square Error (RMSE) and Dynamic Time Warping (DTW) in order to measure the error between the ground truth and the real output. The comparison reveals that our approach has better performance for both the skeletonization stage and the trajectory recovery stage. Moreover, the processing time comparison proves that our system is faster than the existing systems.