• East Asian mathematical journal
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• 제29권3호
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• pp.279-292
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• 2013

It is well known that each kernel function defines a primal-dual interior-point method(IPM). Most of polynomial-time interior-point algorithms for linear optimization(LO) are based on the logarithmic kernel function([2, 11]). In this paper we define a new eligible kernel function and propose a new search direction and proximity function based on this function for LO problems. We show that the new algorithm has ${\mathcal{O}}((log\;p){\sqrt{n}}\;log\;n\;log\;{\frac{n}{\epsilon}})$ and ${\mathcal{O}}((q\;log\;p)^{\frac{3}{2}}{\sqrt{n}}\;log\;{\frac{n}{\epsilon}})$ iteration bound for large- and small-update methods, respectively. These are currently the best known complexity results.

• 호남수학학술지
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• 제35권2호
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• pp.235-249
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• 2013

It is well known that each kernel function defines primal-dual interior-point method (IPM). Most of polynomial-time interior-point algorithms for linear optimization (LO) are based on the logarithmic kernel function ([9]). In this paper we define new eligible kernel function and propose a new search direction and proximity function based on this function for LO problems. We show that the new algorithm has $\mathcal{O}(({\log}\;p)^{\frac{5}{2}}\sqrt{n}{\log}\;n\;{\log}\frac{n}{\epsilon})$ and $\mathcal{O}(q^{\frac{3}{2}}({\log}\;p)^3\sqrt{n}{\log}\;\frac{n}{\epsilon})$ iteration complexity for large- and small-update methods, respectively. These are currently the best known complexity results for such methods.

• 한국IT서비스학회지
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• 제19권1호
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• pp.145-158
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• 2020

With the development and widespread application of online shopping, the number of online consumers has increased. With one click of a mouse, people can buy anything they want without going out and have it sent right to the doors. As consumers benefit from online shopping, people are becoming more concerned about protecting their privacy. In the group buying scenario described in our paper, online shopping was regarded as intra-group communication. To protect the sensitive information of consumers, the polynomial-based encryption key sharing method (Piao et al., 2013; Piao and Kim, 2018) can be applied to online shopping communication. In this paper, we analyze security problems by using a polynomial-based scheme in the following ways : First, in Kamal's attack, they said it does not provide perfect forward and backward secrecy when the members leave or join the group because the secret key can be broken in polynomial time. Second, for simultaneous equations, the leaving node will compute the new secret key if it can be confirmed that the updated new polynomial is recomputed. Third, using Newton's method, attackers can successively find better approximations to the roots of a function. Fourth, the Berlekamp Algorithm can factor polynomials over finite fields and solve the root of the polynomial. Fifth, for a brute-force attack, if the key size is small, brute force can be used to find the root of the polynomial, we need to make a key with appropriately large size to prevent brute force attacks. According to these analyses, we finally recommend the use of a relatively reasonable hash-based mechanism that solves all of the possible security problems and is the most suitable mechanism for our application. The study of adequate and suitable protective methods of consumer security will have academic significance and provide the practical implications.

• 한국컴퓨터정보학회논문지
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• 제21권4호
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• pp.47-54
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• 2016

Cellular formation and layout problem has been known as a NP-hard problem. Because of the algorithm that can be solved exact solution within polynomial time has been unknown yet. This paper suggests a systematic method to be obtain of 2-degree partial directed path from the frequency of consecutive forward order. We apply the modified Kruskal algorithm of minimum spanning tree to be obtain the partial directed path. the proposed reverse constructive algorithm can be solved for this problem with O(mn) time complexity. This algorithm performs same as best known result of heuristic and metaheuristic methods for 4 experimental data.

• 대한전기학회논문지:시스템및제어부문D
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• 제54권9호
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• pp.570-576
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• 2005

In FIR (Finite Impulse Response) filter applications, Nth-band FIR digital filters are known to be important due to their reduced computational requirements. The conventional methods for designing FIR filters use iterative approaches such as the well-known Parks-Mcclellan algorithm. the Parks-Mcclellan algorithm is also used to design Nth-band FIR digital filters. But a disadvantage of the Parks-McClellan algorithm Is that it needs a good amount of design time. This paper describes a direct design method for third-band FIR Filters using Chebyshev polynomial, which provide a reduction in design time over indirect methods such as the Parks-McClellan algorithm. The response of the resulting filter is equi-ripple in passband. The proposed method of design produces a passband response that is equi-ripple to within a minuscule error, compare to that of the Parks-McClellan algorithm.

• 한국컴퓨터정보학회논문지
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• 제19권10호
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• pp.169-173
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• 2014

최적 해를 다항시간으로 얻을 수 있는 알고리즘이 알려져 있지 않은 NP-완전인 상자포장 문제의 일종인 바지선 적재 문제에 대해, Gu$\acute{e}$ret et al.은 $O(m^4)$ 수행 복잡도의 선형계획법으로 해를 얻고자 하였다. 반면에, 본 논문에서는 이득 우선순위로 적재하는 규칙인 O(m log m) 복잡도의 알고리즘을 제안하였다. 제안된 방법은 첫 번째로 이득 우선순위를 결정하였다. 다음으로, 이득 우선순위 물품들을 바지선에 적재하는 방법으로 초기 적재 결과를 얻었다. 마지막으로, 바지선 적재 용량을 미달하는 경우, 이전에 적재된 물품과 미선적된 물품을 상호 교환하여 바지선 적재용량을 충족시켰다. 실험 결과, 제안된 알고리즘은 NP-완전 문제인 바지선 적재 문제에 대해 선형계획법의 $O(m^4)$를 O(m log m)으로 단축시켰다.

• 대한수학회보
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• 제55권1호
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• pp.81-105
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• 2018

In this paper we give two characterisations of the class of reflexive graphs admitting distributive lattice polymorphisms and use these characterisations to address the problem of recognition: we find a polynomial time algorithm to decide if a given reflexive graph G, in which no two vertices have the same neighbourhood, admits a distributive lattice polymorphism.

• 한국지능시스템학회논문지
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• 제15권6호
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• pp.730-735
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• 2005

배낭 문제는 단순한 것 같지만 조합 최적화 문제로서, 다항 시간(polynomial time)에 풀리지 않는 NP-hard 문제이다. 이 문제를 해결하기 위해 기존에는 GA(Genetic Algorithms)를 이용하여 해결하였다. 하지만 기존의 방법은 DNA의 정확한 특성을 고려하지 않아, 실제 실험과의 결과 차이가 발생하고 있다. 본 논문에서는 배낭 문제의 문제점을 해결하기 위해 DNA 컴퓨팅 기법에 DNA 코딩 방법을 적용한 ACO(Algorithm for Code Optimization)를 제안한다. ACO는 배낭 문제 중 (0,1)-배낭 문제에 적용하였고, 그 결과 기존의 방법보다 실험적 오류를 최소화하였으며, 또한 적합한 해를 빠른 시간내에 찾을 수 있었다.

• 한국경영과학회지
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• 제36권2호
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• pp.33-42
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• 2011

Overlay multicasting has received a lot of attention as a core technology for multimedia streaming service. In this paper, we consider the discrete optimal rate allocation problem in multimedia overlay multicasting, which has been proposed by Akbari et al.[2]. The computational complexity of this problem is not known. Thus, we propose a special case which can be solved in polynomial time.

• 한국경영과학회지
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• 제36권2호
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• pp.43-50
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• 2011

We consider the separation problem of the rank-1 Chvatal-Gomory (C-G) inequalities for the 0-1 knapsack problem with the knapsack capacity defined by an additional binary variable, which we call the fixed-charge 0-1 knapsack problem. We analyze the structural properties of the optimal solutions to the separation problem and show that the separation problem can be solved in pseudo-polynomial time. By using the result, we also show that the existence of a pseudo-polynomial time algorithm for the separation problem of the rank-1 C-G inequalities of the ordinary 0-1 knapsack problem.