• 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.

• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.55-69
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• 2024

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}=\{\array{{\frac{p}{2}} && p\;\text{is even} \\ {\frac{p-1}{2}} && p\;\text{is odd,}}$$ and M = {±1, ±2, … ± 𝜌} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling $\frac{{\lambda}(u)+{\lambda}(v)}{2}$ if λ(u) + λ(v) is even and $\frac{{\lambda}(u)+{\lambda}(v)+1}{2}$ if λ(u) + λ(v) is odd such that ${\mid}\bar{\mathbb{s}}_{{\lambda}_1}-\bar{\mathbb{s}}_{{\lambda}^c_1}{\mid}\,{\leq}\,1$ where $\bar{\mathbb{s}}_{{\lambda}_1}$ and $\bar{\mathbb{s}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G with a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling behavior of some union of graphs.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.7
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• pp.2957-2980
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• 2020

Ensemble clustering commonly integrates multiple basic partitions to obtain a more accurate clustering result than a single partition. Specifically, it exists an inevitable problem that the incomplete transformation from the original space to the integrated space. In this paper, a novel ensemble clustering algorithm using a newly reconstructed mapping coefficient (ECRMC) is proposed. In the algorithm, a newly reconstructed mapping coefficient between objects and micro-clusters is designed based on the principle of increasing information entropy to enhance effective information. This can reduce the information loss in the transformation from micro-clusters to the original space. Then the correlation of the micro-clusters is creatively calculated by the Spearman coefficient. Therefore, the revised co-association graph between objects can be built more accurately because the supplementary information can well ensure the completeness of the whole conversion process. Experiment results demonstrate that the ECRMC clustering algorithm has high performance, effectiveness, and feasibility.

• Journal of the Korean Institute of Telematics and Electronics T
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• v.36T no.4
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• pp.71-81
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• 1999

We propose a new CPLD(Complexity Programmable Logic Device) technology mapping algorithm improving run-time under time constraint. In our technology mapping algorithm, a given logic equation is constructed as the DAG(Directed Acyclic Graph) type, then the DAG is reconstructed by replicating the node that outdegree is more than or equal to 2. As a result, it makes delay time and the number of CLBs, run-time to be minimized. Also, after the number of multi-level is defined and cost of each nodes is calculated, the graph is partitioned in order to fit to k that is the number of OR term within CLB. The partitioned nodes are merged through collapsing and bin packing is performed in order to fit to the number of OR term within CLB(Configurable Logic Block). In the results of experiments to MCNC circuits for logic synthesis benchmark, we can shows that proposed technology mapping algorithm reduces run-time and the number of CLBs much more than the TEMPLA.

• Journal of the Institute of Electronics and Information Engineers
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• v.53 no.4
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• pp.37-47
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• 2016

The practical constraints on the commercial FPGAs which contain dedicated wide function multiplexers in their slice structure are incorporated with one of the most advanced FPGA mapping algorithms based on the AIG (And-Inverter Graph), one of the best logic representations in academia. As the first step of the mapping process, cuts are enumerated as intermediate structures. And then, the cuts which can be mapped to the multiplexers are recognized. Without any increased complexity, the delay and area of multiplexers as well as LUTs are calculated after checking the requirements for the tree construction such as symmetry and depth limit against dynamically changing mapping of neighboring nodes. Besides, the root positions of multiplexer trees are identified from the RTL code, and annotated to the AIG as AOs (Auxiliary Outputs). A new AIG embedding the multiplexer tree structures which are intentionally synthesized by Shannon expansion at the AOs, is overlapped with the optimized AIG. The lossless synthesis technique which employs FRAIG (Functionally Reduced AIG) is applied to this approach. The proposed approach and techniques are validated by implementing and applying them to two RISC processor examples, which yielded 13~30% area reduction, and up to 32% delay reduction. The research will be extended to take into account the constraints on the dedicated hardware for carry chains.

• Journal of Institute of Control, Robotics and Systems
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• v.22 no.12
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• pp.1021-1026
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• 2016

The graph-based SLAM (Simultaneous Localization and Mapping) approach has been gaining much attention in SLAM research recently thanks to its ability to provide better maps and full trajectory estimations when compared to the filtering-based SLAM approach. Even though graph-based SLAM requires batch processing causing it to be computationally heavy, recent advancements in optimization and computing power enable it to run fast enough to be used in real-time. However, data association problems still require large amount of computation when building a pose graph. For example, to find loop closures it is necessary to consider the whole history of the robot trajectory and sensor data within the confident range. As a pose graph grows, the number of candidates to be searched also grows. It makes searching the loop closures a bottleneck when solving the SLAM problem. Our approach to alleviate this bottleneck is to sample a limited number of pose nodes in which loop closures are searched. We propose a heuristic for sampling pose nodes that are most advantageous to closing loops by providing a way of ranking pose nodes in order of usefulness for closing loops.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.2
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• pp.234-242
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• 2010

In this paper, we deal with the visualization of graphs, which are one of the most important data structures. As the size of a graph increases, it becomes more difficult to check the graph visually because of the increase of edge intersections. We propose a new method of overcoming such problem. Most of previous studies considered only the minimization of edge intersections, but we additionally pursue to preserve distances between vertices. We present a novel genetic algorithm using an evaluation function based on a weighted sum of two objectives. Our experiments could show effective visualization results.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.1
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• pp.211-230
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• 2022

In image segmentation, for the condition that objects (targets) and background in an image are intertwined or their common boundaries are vague as well as their textures are similar, and the targets in images are greatly variable, the deep learning might be difficult to use. Hence, a new method based on graph theory and guided feathering is proposed. First, it uses a guided feathering algorithm to initially separate the objects from background roughly, then, the image is separated into two different images: foreground image and background image, subsequently, the two images are segmented accurately by using the improved graph-based algorithm respectively, and finally, the two segmented images are merged together as the final segmentation result. For the graph-based new algorithm, it is improved based on MST in three main aspects: (1) the differences between the functions of intra-regional and inter-regional; (2) the function of edge weight; and (3) re-merge mechanism after segmentation in graph mapping. Compared to the traditional algorithms such as region merging, ordinary MST and thresholding, the studied algorithm has the better segmentation accuracy and effect, therefore it has the significant superiority.

• Journal of information and communication convergence engineering
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• v.6 no.4
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• pp.470-474
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• 2008

A well-designed computer network technology produces benefits on several fields within the organization, between the organizations(suborganizations) or among different organizations(suborganizations). Network technology streamlines business processes, decision process. Graphs are useful data structures capable of efficiently representing a variety of networks in the various fields. Metagraph is a like graph theoretic construct introduced recently by Basu and Blanning in which there is set to set mapping in place of node to node as in a conventional graph structure. Metagraph is thus a new type of data structure occupying its popularity among the computer scientists very fast. Every graph is special case of Metagraph. In this paper the authors introduce the notion of Meta-Networking as a new network technological representation, which is having all the capabilities of crisp network as well as few additional capabilities. It is expected that the notion of meta-networking will have huge applications in due course. This paper will play the role of introducing this new concept to the network technologists and scientists.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.709-719
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• 2007

In [8], it is shown that the complete multipartite graph $K_{n(2t)}$ having n partite sets of size 2t, where $n{\geq}6\;and\;t{\geq}1$, has a decomposition into gregarious 6-cycles if $n{\equiv}0,1,3$ or 4 (mod 6). Here, a cycle is called gregarious if it has at most one vertex from any particular partite set. In this paper, when $n{\equiv}0$ or 3 (mod 6), another method using difference set is presented. Furthermore, when $n{\equiv}0$ (mod 6), the decomposition obtained in this paper is ${\infty}-circular$, in the sense that it is invariant under the mapping which keeps the partite set which is indexed by ${\infty}$ fixed and permutes the remaining partite sets cyclically.