• Journal of Communications and Networks
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• v.6 no.1
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• pp.46-59
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• 2004

In this paper, we present two algorithms for efficiently aggregating link state information needed for quality-of-service (QoS) routing. In these algorithms, each edge node in a group is mapped onto a node of a shufflenet or a node of a de Bruijn graph. By this mapping, the number of links for which state information is maintained becomes aN (a is an integer, N is the number of edge nodes) which is significantly smaller than N2 in the full-mesh approach. Our algorithms also can support asymmetric link state parameters which are common in practice, while many previous algorithms such as the spanning tree approach can be applied only to networks with symmetric link state parameters. Experimental results show that the performance of our shufflenet algorithm is close to that of the full-mesh approach in terms of the accuracy of bandwidth and delay information, with only a much smaller amount of information. On the other hand, although it is not as good as the shufflenet approach, the de Bruijn algorithm also performs far better than the star approach which is one of the most widely accepted schemes. The de Bruijn algorithm needs smaller computational complexity than most previous algorithms for asymmetric networks, including the shufflenet algorithm.

• 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 the Korean Mathematical Society
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• v.48 no.1
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• pp.105-115
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• 2011

Let f be a function which assigns a positive integer f(v) to each vertex v $\in$ V (G), let r, s and t be non-negative integers. An f-coloring of G is an edge-coloring of G such that each vertex v $\in$ V (G) has at most f(v) incident edges colored with the same color. The minimum number of colors needed to f-color G is called the f-chromatic index of G and denoted by ${\chi}'_f$(G). An [r, s, t; f]-coloring of a graph G is a mapping c from V(G) $\bigcup$ E(G) to the color set C = {0, 1, $\ldots$; k - 1} such that |c($v_i$) - c($v_j$ )| $\geq$ r for every two adjacent vertices $v_i$ and $v_j$, |c($e_i$ - c($e_j$)| $\geq$ s and ${\alpha}(v_i)$ $\leq$ f($v_i$) for all $v_i$ $\in$ V (G), ${\alpha}$ $\in$ C where ${\alpha}(v_i)$ denotes the number of ${\alpha}$-edges incident with the vertex $v_i$ and $e_i$, $e_j$ are edges which are incident with $v_i$ but colored with different colors, |c($e_i$)-c($v_j$)| $\geq$ t for all pairs of incident vertices and edges. The minimum k such that G has an [r, s, t; f]-coloring with k colors is defined as the [r, s, t; f]-chromatic number and denoted by ${\chi}_{r,s,t;f}$ (G). In this paper, we present some general bounds for [r, s, t; f]-coloring firstly. After that, we obtain some important properties under the restriction min{r, s, t} = 0 or min{r, s, t} = 1. Finally, we present some problems for further research.

• Journal of Acupuncture Research
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• v.20 no.1
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• pp.22-34
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• 2003

Objective : To ascertain whether the concept of the treatment side is associated with changes in the blind spot mapping that represents the brain function. Methods : Among the outpatients who visited to Department of Acupuncture & Moxibustion, National Medical Center from March 2002 to October 2002, we selected 40 clinical trial volunteers that showed right side physiological blind spot more enlarged than left, and underwent the examinations of Department of Opthalmology, National Medical Center for ruling out the pathological conditions. Physiological blind spot maps were used as an integer of brain activity before and after electroacupuncture application on the unilateral ST36 meridian point by dividing 40 subjects into two comparative groups for double-blind controlled study. Results: The significant changes in the blind spots were observed. Electroacupuncture application on the ipsilateral or contralateral ST36 of an enlargement cortical map were associated with the concept of determining the treatment side. In the case of electroacupuncture application on the ipsilateral side of an enlarged blind spot, there were decrease of $4.11{\pm}8.56cm$(17.3%) in blind spot perimetry length(p < 0.05). In the case of contralateral side, there were increase of $3.19{\pm}5.40cm$(13.7%) in blind spot perimetry length(p<0.05). The Differences were statistically significant(p<0.05). Conclusions: We found that eletroacupuncture application was associated with an increase or decrease in the brain function in the view of blind spot changes depending on the treatment side. These results suggest that the traditional acupuncture therapeutic strategy with determining the treatment side has clinical significance in the view of the brain function.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.42 no.3 s.303
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• pp.39-52
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• 2005

In this paper, a registration method is presented to register partial 3D point clouds, acquired from a multi-view camera, for 3D reconstruction of an indoor environment. In general, conventional registration methods require a high computational complexity and much time for registration. Moreover, these methods are not robust for 3D point cloud which has comparatively low precision. To overcome these drawbacks, a projection-based registration method is proposed. First, depth images are refined based on temporal property by excluding 3D points with a large variation, and spatial property by filling up holes referring neighboring 3D points. Second, 3D point clouds acquired from two views are projected onto the same image plane, and two-step integer mapping is applied to enable modified KLT (Kanade-Lucas-Tomasi) to find correspondences. Then, fine registration is carried out through minimizing distance errors based on adaptive search range. Finally, we calculate a final color referring colors of corresponding points and reconstruct an indoor environment by applying the above procedure to consecutive scenes. The proposed method not only reduces computational complexity by searching for correspondences on a 2D image plane, but also enables effective registration even for 3D points which have low precision. Furthermore, only a few color and depth images are needed to reconstruct an indoor environment.