• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.7
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• pp.2325-2349
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• 2014

Network virtualization technology plays a key role in cloud computing, which serves as an effective approach for provisioning a flexible and highly adaptable shared substrate network to satisfy the demands of various applications or services. Recently, the problem of mapping a virtual network (VN) onto a substrate network has been addressed by various algorithms. However, these algorithms are typically efficient for unicast service-oriented virtual networks, and generally not applicable to multicast service-oriented virtual networks (MVNs). Furthermore, the survivable MVN mapping (SMVNM) problem that considers the survivability of MVN has not been studied and is also the focus of this work. In this research, we discuss SMVNM problem under regional failures in the substrate network and propose an efficient algorithm for solving this problem. We first propose a framework and formulate the SMVNM problem with the objective of minimizing mapping cost by using mixed integer linear programming. Then we design an efficient heuristic to solve this problem and introduce several optimizations to achieve the better mapping solutions. We validate and evaluate our framework and algorithms by conducting extensive simulations on different realistic networks under various scenarios, and by comparing with existing approaches. Our simulation experiments and results show that our approach outperforms existing solutions.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.2 no.2
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• pp.133-138
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• 2002

In this paper, we propose an integrated GUI environment of parallel fuzzy inference system fur pattern classification of remote sensing data. In this, as 4 fuzzy variables in condition part and 104 fuzzy rules are used, a real time and parallel approach is required. For frost fuzzy computation, we use the scan line conversion algorithm to convert lines of each fuzzy linguistic term to the closest integer pixels. We design 4 fuzzy processor unit to be operated in parallel by using FPGA. As a GUI environment, PCI transmission, image data pre-processing, integer pixel mapping and fuzzy membership tuning are considered. This system can be used in a pattern classification system requiring a rapid inference time in a real-time.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.10
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• pp.4640-4661
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• 2018

To cope with the explosive growth of Internet services, Service Function Chaining (SFC) based on Software-defined Networking (SDN) is an emerging and promising technology that has been suggested to meet this challenge. Determining the placement of Virtual Network Functions (VNFs) and routing paths that optimize the network utilization and resource consumption is a challenging problem, particularly without violating service level agreements (SLAs). This problem is called the optimal SFC placement problem and an Integer Linear Programming (ILP) formulation is provided. A greedy heuristic solution is also provided based on an improved two-step mapping algorithm. The obtained experimental results show that the proposed algorithm can automatically place VNFs at the optimal locations and find the optimal routing paths for each online request. This algorithm can increase the average request acceptance rate by about 17.6% and provide more than 20-fold reduction of the computational complexity compared to the Greedy algorithm. The feasibility of this approach is demonstrated via NetFPGA-10G prototype implementation.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.6
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• pp.75-80
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• 2023

We show the design of fast invertible block transforms that can replace the DCT in future wireless and portable computing application. This is called binDCT. In binDCT, both the forward and the inverse transforms can be implemented using only binary shift and addition operation. And the binDCT inherits all desirable DCT characteristics such as high coding gain, no DC leakage, symmetric basis functions, and recursive construction. The binDCT also inherits all lifting properties such as fast implementations, invertible integer-to-integer mapping, in-place computation. Thus, this method has advantage of fast implementation for complex DCT calculations. In this paper, we present computation costs and performance analysis between DCT and binDCT using Shapiro's EZW.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.8
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• pp.3701-3727
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• 2016

Recently Service Function Chaining (SFC) is promising to innovate the network service mode in modern networks. However, a feasible implementation of SFC is still difficult due to the need to achieve functional equivalence with traditional modes without sacrificing performance or increasing network complexity. In this paper, we present a configurable network service chaining (CNSC) mechanism to provide services for network traffics in a flexible and optimal way. Firstly, we formulate the problem of network service chaining and design an effective service chain construction framework based on integrating software-defined networking (SDN) with network functions virtualization (NFV). Then, we model the service path computation problem as an integer liner optimization problem and propose an algorithm named SPCM to cooperatively combine service function instances with a network utility maximum policy. In the procedure of SPCM, we achieve the service node mapping by defining a service capacity matrix for substrate nodes, and work out the optimal link mapping policies with segment routing. Finally, the simulation results indicate that the average request acceptance ratio and resources utilization ratio can reach above 85% and 75% by our SPCM algorithm, respectively. Upon the prototype system, it is demonstrated that CNSC outperforms other approaches and can provide flexible and scalable network services.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.673-688
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• 2011

Let $n{\geq}2$ be an even integer. We investigate that if an odd mapping f : X ${\rightarrow}$ Y satisfies the following equation $2_{n-2}C_{\frac{n}{2}-1}rf\(\sum\limits^n_{j=1}{\frac{x_j}{r}}\)\;+\;{\sum\limits_{i_k{\in}\{0,1\} \atop {{\sum}^n_{k=1}\;i_k={\frac{n}{2}}}}\;rf\(\sum\limits^n_{i=1}(-1)^{i_k}{\frac{x_i}{r}}\)=2_{n-2}C_{{\frac{n}{2}}-1}\sum\limits^n_{i=1}f(x_i),$ then f : X ${\rightarrow}$ Y is additive, where $r{\in}R$. We also prove the stability in normed group by using shadowing property and the Hyers-Ulam stability of the functional equation in Banach spaces and in Banach modules over unital C-algebras. As an application, we show that every almost linear bijection h : A ${\rightarrow}$ B of unital $C^*$-algebras A and B is a $C^*$-algebra isomorphism when $h(\frac{2^s}{r^s}uy)=h(\frac{2^s}{r^s}u)h(y)$ for all unitaries u ${\in}$ A, all y ${\in}$ A, and s = 0, 1, 2,....

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.413-424
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• 2008

In [21], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\parallel}\frac{1}{n}\sum\limits_{i=1}^{n}x_i{\parallel}^2+\sum\limits_{i=1}^{n}{\parallel}x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j{\parallel}^2=\sum\limits_{i=1}^{n}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\dots},x_n{\in}V$. We consider the functional equation $$nf(\frac{1}{n}\sum\limits^n_{i=1}x_i)+\sum\limits_{i=1}^{n}f(x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j)=\sum\limits_{i=1}^nf(x_i)$$ Using fixed point methods, we prove the generalized Hyers-Ulam stability of the functional equation $$(1)\;2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})=f(x)+f(y)$$.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2021.10a
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• pp.236-239
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• 2021

With the growth of AI technology, the scale of Knowledge Graphs continues to be expanded. Knowledge Graphs are mainly expressed as RDF representations that consist of connected triples. Many RDF storages compress and transform RDF triples into the condensed IDs. However, if we try to transform a large scale of RDF triples, it occurs the high processing time and memory overhead because it needs to search the large ID mapping table. In this paper, we propose the method of converting RDF triples using Hash-based ID mapping tables with MapReduce, which is the software framework with a parallel, distributed algorithm. Our proposed method not only transforms RDF triples into Integer-based IDs, but also improves the conversion speed and memory overhead. As a result of our experiment with the proposed method for LUBM, the size of the dataset is reduced by about 3.8 times and the conversion time was spent about 106 seconds.

• Bulletin of the Korean Mathematical Society
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• v.33 no.2
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• pp.221-228
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• 1996

Throughout, R will represent an associative ring with center Z(R). A module X is said to be n-torsionfree, where n is an integer, if nx = 0, $x \in X$ implies x = 0. An additive mapping $D : R \to X$, where X is a left R-module, will be called a Jordan left derivation if $D(a^2) = 2aD(a), a \in R$. M. Bresar and J. Vukman [1] showed that the existence of a nonzero Jordan left derivation of R into X implies R is commutative if X is a 2-torsionfree and 3-torsionfree left R-module.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.959-970
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• 2016

In this paper, we generalize the stability for an n-dimensional cubic functional equation in Banach space to set-valued dynamics. Let $n{\geq}2$ be an integer. We define the n-dimensional cubic set-valued functional equation given by $$f(2{{\sum}_{i=1}^{n-1}}x_i+x_n){\oplus}f(2{{\sum}_{i=1}^{n-1}}x_i-x_n){\oplus}4{{\sum}_{i=1}^{n-1}}f(x_i)\\=16f({{\sum}_{i=1}^{n-1}}x_i){\oplus}2{{\sum}_{i=1}^{n-1}}(f(x_i+x_n){\oplus}f(x_i-x_n)).$$ We first prove that the solution of the n-dimensional cubic set-valued functional equation is actually the cubic set-valued mapping in [6]. We prove the Hyers-Ulam stability for the set-valued functional equation.