• Journal of Electrical Engineering and information Science
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• 제3권3호
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• pp.281-285
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• 1998

Consider the two-dimensional sorted-set convex hull problem: Given N points in a plane sorted by the x coordinates, compute the convex hull of the points. We propose an O(logNlog logN)-time algorithm that solves the sorted-set convex hull problem on an N\ulcorner\ulcorner${\times}$N\ulcorner\ulcorner reconfigurable mesh. The best known algorithm for the problem on an N\ulcorner\ulcorner${\times}$N\ulcorner\ulcorner reconfigurable mesh takes O(log\ulcornerN) time. Although there is a constant-time algorithm on an N${\times}$N reconfigurable mesh for general two-dimensional convex hull problem, the general convex hull problem requires Θ(N\ulcorner\ulcorner) time on an N\ulcorner\ulcorner${\times}$N\ulcorner\ulcorner reconfigurable mesh due to bandwidth constraints.

• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.535-543
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• 1997

The application of Hadamard matrix to the paral-lel routings on the hypercube network was presented by Rabin. In this matrix every two rows differ from each other by exactly n/2 positions. A set of n disjoint paths on n-dimensional hypercube net-work was designed using this peculiar property of Hadamard ma-trix. Then the data is dispersed into n packets and these n packet are transmitted along these n disjoint paths. In this paper Rabin's routing algorithm is analyzed in terms of covering problem and as-signment problem. Finally we conclude that n packets dispersed are placed in well-distributed positions during transmisson and the ran-domly selected paths are almost a set of n edge-disjoint paths with high probability.

• 대한수학회논문집
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• 제22권3호
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• pp.383-389
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• 2007

In this paper we examine the hyperinvariant subspace problem for quasi-n-hyponormal operators. The main result on this problem is as follows. If T = N + K is such that N is a quasi-n-hyponormal operator whose spectrum contains an exposed arc and K belongs to the Schatten p-ideal then T has a non-trivial hyperinvariant subspace.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.141-154
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• 2007

The connectivity problem is a fundamental problem in graph theory. The best known algorithm to solve the connectivity problem on general graphs with n vertices and m edges takes $O(K(G)mn^{1.5})$ time, where K(G) is the vertex connectivity of G. In this paper, an efficient algorithm is designed to solve vertex connectivity problem, which takes $O(n^2)$ time and O(n) space for a trapezoid graph.

• 대한수학회보
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• 제44권2호
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• pp.337-350
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• 2007

Given a collection of complex numbers ${\gamma}{\equiv}\{{\gamma}ij\}$ $(0{\leq}i+j{\leq}2n,\;|i-j|{\leq}n)$ with ${\gamma}00>0\;and\;{\gamma}ji=\bar{\gamma}ij$, we consider the moment problem for ${\gamma}$ in the case of n=2, which is referred to Embry quartic moment problem. In this note we give a partial solution for the nonsingular case of Embry quartic moment problem.

• 한국컴퓨터정보학회논문지
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• 제20권7호
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• pp.33-40
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• 2015

The time slot assignment problem (TSAP) or Satellite Communications scheduling problem (SCSP) for a satellite performs $n{\times}n$ ground station data traffic switching has been known NP-hard problem. This paper suggests $O(n^2)$ time complexity algorithm for TSAP of a satellite that performs $n^2{\times}n^2$ ground station data traffic switching. This problem is more difficult than $n{\times}n$ TSAP as NP-hard problem. Firstly, we compute the average traffic for n-transponder's basic coverage zone and applies ground station exchange method that swap the ground stations until all of the transponders have a average value as possible. Nextly, we transform the D matrix to $D_{LB}$ traffic matrix that sum of rows and columns all of transponders have LB. Finally, we select the maximum traffic of row and column in $D_{LB}$, then decide the duration of kth switch mode to minimum traffic from selected values. The proposed algorithm can be get the optimal solution for experimental data.

• International Journal of Computer Science & Network Security
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• 제24권9호
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• pp.105-110
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• 2024

Nowadays, permutation problems with large state spaces and the path to solution is irrelevant such as N-Queens problem has the same general property for many important applications such as integrated-circuit design, factory-floor layout, job-shop scheduling, automatic programming, telecommunications network optimization, vehicle routing, and portfolio management. Therefore, methods which are able to find a solution are very important. Genetic algorithm (GA) is one the most well-known methods for solving N-Queens problem and applicable to a wide range of permutation problems. In the absence of specialized solution for a particular problem, genetic algorithm would be efficient. But holism and random choices cause problem for genetic algorithm in searching large state spaces. So, the efficiency of this algorithm would be demoted when the size of state space of the problem grows exponentially. In this paper, the new method presented based on genetic algorithm to cover this weakness. This new method is trying to provide partial view for genetic algorithm by locally searching the state space. This may cause genetic algorithm to take shorter steps toward the solution. To find the first solution and other solutions in N-Queens problem using proposed method: dividing N-Queens problem into subproblems, which configuring initial population of genetic algorithm. The proposed method is evaluated and compares it with two similar methods that indicate the amount of performance improvement.

• 융합보안논문지
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• 제14권7호
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• pp.59-64
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• 2014

이 논문에서는 고정된 개수를 가진 bin들을 이용하여 실행 복잡도가 $p(n){\cdot}2^{O(\sqrt{n})}$인 알고리즘을 제시한다, 여기서 x는 (5)n개의 객체들에 대한 리스트의 길이에 대한 총 비트 수를 나타낸다. 이러한 방법은 수치적 크기나 비중의 합의 리스트를 이용하는 여러 가지 최적화 알고리즘이나 결정 문제등에 적용할 수 있다. 이 논문에서 제시한 알고리즘은 의사-다항식(pseudo-polynomial) 시간을 갖는 NP-Complete의 많은 문제들을 결정적인 서브-지수 시간에 해결할 수 있은 가능성을 제시한다. 여기서 제시한 알고리즘을 이용하여 생명공학의 유전자 분석에 적용하려고 한다.

• 대한산업공학회지
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• 제40권4호
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• pp.396-403
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• 2014

The multi-divisional knapsack problem is defined as a binary knapsack problem where each mutually exclusive division has its own capacity. In this paper, we present an extension of the multi-divisional knapsack problem that has generalized multiple-choice constraints. We explore the linear programming relaxation (P) of this extended problem and identify some properties of problem (P). Then, we develop a transformation which converts the problem (P) into an LP knapsack problem and derive the optimal solutions of problem (P) from those of the converted LP knapsack problem. The solution procedures have a worst case computational complexity of order $O(n^2{\log}\;n)$, where n is the total number of variables. We illustrate a numerical example and discuss some variations of problem (P).

• 대한수학회지
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• 제56권4호
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• pp.1001-1016
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• 2019

We are concerned with optimization methods for the $L^2$-Wasserstein least squares problem of Gaussian measures (alternatively the n-coupling problem). Based on its equivalent form on the convex cone of positive definite matrices of fixed size and the strict convexity of the variance function, we are able to present an implementable (accelerated) gradient method for finding the unique minimizer. Its global convergence rate analysis is provided according to the derived upper bound of Lipschitz constants of the gradient function.