• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.13-29
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• 2021

For a graph G = (V, E), a vertex coloring (or, simply, a coloring) of G is a function C : V (G) → {1, 2, …, k} (using the non-negative integers {1, 2, …, k} as colors). We say that a coloring of a graph G is injective if for every vertex v ∈ V (G), all the neighbors of v are assigned with distinct colors. The injective chromatic number χi(G) of a graph G is the least k such that there is an injective k-coloring [6]. In this paper, we study a natural variation of the injective coloring problem: coloring the edges of a graph under the same constraints (alternatively, to investigate the injective chromatic number of line graphs), we define the k- injective edge coloring of a graph G as a mapping C : E(G) → {1, 2, …, k}, such that for every edge e ∈ E(G), all the neighbors edges of e are assigned with distinct colors. The injective chromatic index χ′in(G) of G is the least positive integer k such that G has k- injective edge coloring, exact values of the injective chromatic index of different families of graphs are obtained, some related results and bounds are established. Finally, we define the injective clique number ωin and state a conjecture, that, for any graph G, ωin ≤ χ′in(G) ≤ ωin + 2.

• Kyungpook Mathematical Journal
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• v.56 no.4
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• pp.1103-1113
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• 2016

In this paper, we study a directed simple graph ${\Gamma}_S(N)$ for a near-ring N, where the set $V^*(N)$ of vertices is the set of all left N-subsets of N with nonzero left annihilators and for any two distinct vertices $I,J{\in}V^*(N)$, I is adjacent to J if and only if IJ = 0. Here, we deal with the diameter, girth and coloring of the graph ${\Gamma}_S(N)$. Moreover, we prove a sufficient condition for occurrence of a regular element of the near-ring N in the left annihilator of some vertex in the strong zero-divisor graph ${\Gamma}_S(N)$.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.1037-1067
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• 2017

Motzkin and Straus established a close connection between the maximum clique problem and a solution (namely graph-Lagrangian) to the maximum value of a class of homogeneous quadratic multilinear functions over the standard simplex of the Euclidean space in 1965. This connection and its extensions were successfully employed in optimization to provide heuristics for the maximum clique problem in graphs. It is useful in practice if similar results hold for hypergraphs. In this paper, we develop a homogeneous multilinear function based on the structure of hypergraphs and their complement hypergraphs. Its maximum value generalizes the graph-Lagrangian. Specifically, we establish a connection between the clique number and the generalized graph-Lagrangian of 3-uniform graphs, which supports the conjecture posed in this paper.

• Journal of Korean Society of Rural Planning
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• v.6 no.2 s.12
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• pp.12-19
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• 2000

Irrigation pipeline networks consist mainly of buried pipes and are therefore relatively free from topographic constraints. Installation of irrigation pipeline systems is increasing since the systems have several advantages compared to open channel systems. To achieve economic design of pipeline networks, the layout should meet several conditions such as shortest path, maximum flow, and least cost. Graph theory is mathematical tool which enable to find out optimum layout for complicated network systems. In this study, applicability of graph theory to figure out optimum layout of irrigation pipeline networks was evaluated.

• Proceedings of the Korea Information Processing Society Conference
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• 2023.05a
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• pp.383-385
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• 2023

Single-machine-based 그래프 엔진의 state-of-the-art 모델인 RealGraph 는 쓰레드를 이용한 병렬화로 성능을 향상하였으나 쓰레드 내부에서의 병렬성은 고려되지 않았다. 본 논문은 SIMD 명령어를 이용해 RealGraph 의 병렬성을 향상시켰다. 쓰레드 내부의 효율성을 높이기 위해 RealGraph 의 구조와 그래프 알고리즘의 분석을 통한 SIMD 명령어의 적용 가능한 영역을 탐색하였다. 실험으로 SIMD 명령어의 적용을 통해 쓰레드 내부에서 벡터 연산을 수행하여 평균 7.6%, 11.7%, 9.2%의 수행 시간 단축을 이끌어냈으며 SIMD 명령어의 적용이 그래프 엔진의 분석 성능에 얼마나 도움이 될 수 있는지 확인하였다.

• Journal of Korea Multimedia Society
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• v.3 no.1
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• pp.77-90
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• 2000

Real-Time verification is a procedure that verifies the correctness of specification related to requirement in time as well as in logic. One serious problem encountered in the verification task is that the state space grows exponentially owing to the unboundedness of time, which is termed the state space explosion problem. In this paper, we propose a real-time verification technique checking the correctness of specification by showing that a system model described in timed automata is equivalent to the characteristic of system property specified in timed modal-mu calculus. For this, we propose a local model checking method based on the value of the formula in initial state with constructing product graph concerned to only the nodes needed for verification process. Since this method does not search for every state of system model, the state space is reduced drastically so that the proposed method can be applied effectively to real-time system verification.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.17 no.12
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• pp.3383-3397
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• 2023

Scene graphs serve as semantic abstractions of images and play a crucial role in enhancing visual comprehension and reasoning. However, the performance of Scene Graph Generation is often compromised when working with biased data in real-world situations. While many existing systems focus on a single stage of learning for both feature extraction and classification, some employ Class-Balancing strategies, such as Re-weighting, Data Resampling, and Transfer Learning from head to tail. In this paper, we propose a novel approach that decouples the feature extraction and classification phases of the scene graph generation process. For feature extraction, we leverage a transformer-based architecture and design an adaptive calibration function specifically for predicate classification. This function enables us to dynamically adjust the classification scores for each predicate category. Additionally, we introduce a Distribution Alignment technique that effectively balances the class distribution after the feature extraction phase reaches a stable state, thereby facilitating the retraining of the classification head. Importantly, our Distribution Alignment strategy is model-independent and does not require additional supervision, making it applicable to a wide range of SGG models. Using the scene graph diagnostic toolkit on Visual Genome and several popular models, we achieved significant improvements over the previous state-of-the-art methods with our model. Compared to the TDE model, our model improved mR@100 by 70.5% for PredCls, by 84.0% for SGCls, and by 97.6% for SGDet tasks.

• Kyungpook Mathematical Journal
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• v.24 no.2
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• pp.101-113
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• 1984

• The KIPS Transactions:PartB
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• v.15B no.2
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• pp.159-170
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• 2008

Nowadays, one of the important functionalities required from robot task planners is to generate plans to compose existing component services into a new service. In this paper, we introduce the design and implementation of a heuristic search planner, JPLAN, as a kernel module for component service composition. JPLAN uses a local search algorithm and planning graph heuristics. The local search algorithm, EHC+, is an extended version of the Enforced Hill-Climbing(EHC) which have shown high efficiency applied in state-space planners including FF. It requires some amount of additional local search, but it is expected to reduce overall amount of search to arrive at a goal state and get shorter plans. We also present some effective heuristic extraction methods which are necessarily needed for search on a large state-space. The heuristic extraction methods utilize planning graphs that have been first used for plan generation in Graphplan. We introduce some planning graph heuristics and then analyze their effects on plan generation through experiments.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.36C no.10
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• pp.47-55
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• 1999

In this paper, a new function hazard elimination algorithm is proposed for asynchronous circuit synthesis. In previous approach, function hazard is eliminated by using state graph which is obtained from the state assignment on STG(signal transition graph) representing transition relationship among signals. These algorithms can use conventional hazard removal and synthesis method applied in synchronous system, but it has much computational complexity and takes much time to handle the state graph. Although some hazard elimination algorithm from STG were proposed, it could not reduce the area overhead due to the addition of new signals. The proposed algorithm eliminate function hazard directly on STG and also control the number of minterms and product-term of added signal in order to minimize the area overhead. Experimental results on benchmark data shows that overall circuit area after hazard elimination is decreased about 15% on the average than that of previous method.