• Journal of Korea Spatial Information System Society
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• v.11 no.4
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• pp.39-46
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• 2009

Generally, Path-finding algorithms which use heuristic function may occur a problem of the increase of exploring cost in case of that there is no way determined by heuristic function or there are 2 way more which have almost same cost. In this paper, we propose an abstract graph for path-finding with dynamic information. The abstract graph is a simple graph as real road network is abstracted. The abstract graph is created by fixed-size cells and real road network. Path-finding with the abstract graph is composed of two step searching, path-finding on the abstract graph and on the real road network. We performed path-finding algorithm with the abstract graph against A* algorithm based on fixed-size cells on road network that consists of 106,254 edges. In result of evaluation of performance, cost of exploring in path-finding with the abstract graph is about 3~30% less than A* algorithm based on fixed-size cells. Quality of path in path-finding with the abstract graph is, However, about 1.5~6.6% more than A* algorithm based on fixed-size cells because edges eliminated are not candidates for path-finding.

• The Mathematical Education
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• v.13 no.2
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• pp.6-10
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• 1974

We consider 'ordinary' graphs: that is, finite undirected graphs with no loops or multiple edges. An intersection representation of a graph G is a function r from V(G), the set of vertices of G, into a family of sets S such that distinct points $\chi$$_{\alpha}$ and $\chi$$_{\beta}$/ of V(G) are. neighbors in G precisely when ${\gamma}$($\chi$$_{\alpha}$)∩${\gamma}$($\chi$$_{\beta}$/)$\neq$ø, A graph G is a rigid circuit grouph if every cycle in G has at least one triangular chord in G. In this paper we consider the main theorem; A graph G has an intersection representation by arcs on an acyclic graph if and only if is a normal rigid circuit graph.uit graph.d circuit graph.uit graph.

• Honam Mathematical Journal
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• v.37 no.3
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• pp.361-376
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• 2015

We have calculated the volume of the graph polytopes associated with several types of graphs.

• Proceedings of the IEEK Conference
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• 2000.09a
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• pp.671-674
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• 2000

In this paper, we present a robust global registration algorithm for multi-frame image mosaics. When we perform a pair-wise registration recovering a projective transformation between two consecutive frames, severe mis-registration among multiple frames, which are not consecutive, can be detected. It is because the concatenation of those pair-wise transformations leads to global alignment errors. To overcome those mis-registrations, we propose a new algorithm using multiple frames for constructing image mosaics. We use a graph to represent the temporal and spatial connectivity and show that global registration can be obtained through the search for an optimal path in the constructed graph. The definition of an adequate objective function characterizing the global registration provides a direct manipulation of the graph. In the presence of moving objects, especially large ones compared with low texture backgrounds, by using the likelihood ratio as the objective function, we can deal with some of the most challenging videos like basketball or soccer Moreover, the algorithm can be parallelized so it can be more efficiently implemented. Finally, we give some experimental results from real videos.

• International Journal of Contents
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• v.10 no.1
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• pp.23-28
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• 2014

When developing a classifier using various objective functions, it is important to compare the performances of the classifiers. Although there are statistical analyses of objective functions for classifiers, simulation results can provide us with direct comparison results and in this case, a comparison criterion is considerably critical. A Receiver Operating Characteristics (ROC) graph is a simulation technique for comparing classifiers and selecting a better one based on a performance. In this paper, we adopt the ROC graph to compare classifiers trained by mean-squared error, cross-entropy error, classification figure of merit, and the n-th order extension of cross-entropy error functions. After the training of feed-forward neural networks using the CEDAR database, the ROC graphs are plotted to help us identify which objective function is better.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1305-1315
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• 2022

Let u be a function on a connected finite graph G = (V, E). We consider the mean field equation (1) $-{\Delta}u={\rho}\({\frac{he^u}{\int_Vhe^ud{\mu}}}-{\frac{1}{{\mid}V{\mid}}}\),$ where ∆ is 𝜇-Laplacian on the graph, 𝜌 ∈ ℝ\{0}, h : V → ℝ⁺ is a function satisfying min_x∈V h(x) > 0. Following Sun and Wang [15], we use the method of Brouwer degree to prove the existence of solutions to the mean field equation (1). Firstly, we prove the compactness result and conclude that every solution to the equation (1) is uniformly bounded. Then the Brouwer degree can be well defined. Secondly, we calculate the Brouwer degree for the equation (1), say $$d_{{\rho},h}=\{{-1,\;{\rho}>0, \atop 1,\;{\rho}<0.}$$ Consequently, the equation (1) has at least one solution due to the Brouwer degree d_𝜌,h ≠ 0.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.5
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• pp.2084-2100
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• 2020

Operating system (OS) kernel function call graphs have been widely used in OS analysis and defense. However, most existing methods and tools for generating function call graphs are designed for application programs, and cannot be used for generating OS kernel function call graphs. This paper proposes a virtualization-based call graph generation method called Acquire in Trap (AIT). When target kernel functions are called, AIT dynamically initiates a system trap with the help of a virtualization technique. It then analyzes and records the calling relationships for trap handling by traversing the kernel stacks and the code space. Our experimental results show that the proposed method is feasible for both Linux and Windows OSs, including 32 and 64-bit versions, with high recall and precision rates. AIT is independent of the source code, compiler and OS kernel architecture, and is a universal method for generating OS kernel function call graphs.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1301-1324
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• 2006

The affine homogeneous hypersurface in ${\mathbb{R}}^{n+1}$, which is a graph of a function $F:{\mathbb{R}}^n{\rightarrow}{\mathbb{R}}$ with |det DdF|=1, corresponds to a complete unimodular left symmetric algebra with a nondegenerate Hessian type inner product. We will investigate the condition for the domain over the homogeneous hypersurface to be homogeneous through an extension of the complete unimodular left symmetric algebra, which is called the graph extension.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.223-237
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• 2021

Let G = (V (G), E(G)) be a graph and let g : V (G) → S3 be a function. For each edge xy assign the label r where r is the remainder when o(g(x)) is divided by o(g(y)) or o(g(y)) is divided by o(g(x)) according as o(g(x)) ≥ o(g(y)) or o(g(y)) ≥ o(g(x)). The function g is called a group S3 cordial remainder labeling of G if |vg(i)-vg(j)| ≤ 1 and |eg(1)-eg(0)| ≤ 1, where vg(j) denotes the number of vertices labeled with j and eg(i) denotes the number of edges labeled with i (i = 0, 1). A graph G which admits a group S3 cordial remainder labeling is called a group S3 cordial remainder graph. In this paper, we prove that square of the path, duplication of a vertex by a new edge in path and cycle graphs, duplication of an edge by a new vertex in path and cycle graphs and total graph of cycle and path graphs admit a group S3 cordial remainder labeling.

• Communications of Mathematical Education
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• v.22 no.2
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• pp.125-136
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• 2008

There are different perspectives on a function graph. For instance, a parabola is defined by movement of a ball in physics and by quadratic function in mathematics. This study deals with the turtle motion, which is local and intrinsic, and the construction of function graphs with mathematical experiments in a microworld. This paper concerns with a function graph which is in the curriculum or in the history of mathematics. In view of pre-calculus, we introduce activities of mathematization about formalizing of length and area of function graphs without knowledge of calculus.