• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.23-30
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• 2002

본 연구는 추가제약이 있는 최소 신장나무 문제(Constrained Minimum Spanning Tree : CMST문제)에 대한 유사다항시간 알고리듬 및 근사 해법 개발에 관한 것이다. CMST문제는 NP-hard문제임이 이미 증명되었으며, 이후 이 문제에 대해서는 근사해법 개발이 주된 관심이 되어왔다 [Ravi and Goemans 96]는 다항시간 근사 해법(PTAS)을 이미 개발하였고, [Marathe et at 98]은 가능해(feasible solution)는 아니지만, 앞으로 서술할 $(1+1/\varepsilon,\;+\epsilon)$사해를 구하는 완전다항시간 근사해법 (FPTAS)을 제시하였다. 이와는 달리 [Papa. and Yan, 00]는 파레토 근사 최적해를 구하는 FPTAS를 제시하였는데, 본 연구는 이들의 연구에서 주로 의존하고 있는 행렬-나무 정리(Tree-Matrix Theorem)를 보다 일반화하여, CMST문제에 대한 유사다항시간 알고리듬과 $(1+\varepsilon,\;1+\epsilon)$근사해를 구하는 FPTAS를 제시할 것이다.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.6
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• pp.188-198
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• 1994

The distributed arithmetic approach has been commonly recognized as an efficient method to implement the inner-product type of computation with fixed coefficients such as DCT/IDCT. This paper presents a novel architecture and the implementation of 2-D DCT/IDCT VLSI chip based on distributed arithmetic. The main feature of the proposed architecture is a fully 2-bit serial pipeline and parallel structure with memory-based signal processing circuitry, which is efficient to the implementation of the bit-serial operation of distributed arithmetic. All modules of the proposed architecture are designed with NP-dynamic circuitry to reduce the power consumption and to increase the performance. This chip is applicable in HDTV systems working at video sampling rate up to 75 MHz.

• Proceedings of the Korea Information Processing Society Conference
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• 2000.10b
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• pp.1373-1376
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• 2000

외판원 문제(Traveling Salesman Problem)는 주어진 n개의 도시들과 그 도시들간의 거리 비용이 주어졌을 매, 처음 출발도시에서부터 정확히 한 도시는 한 번씩만 방문하여 다시 출발도시로 돌아오면서 방문한 도시들을 연결하는 최소의 비용이 드는 경로를 찾는 문제로 최적해(optimal value)를 구하는 것은 전형적인 NP-완전 문제중의 하나이다[2,4,5, 8]. 따라서 이들의 수행시간을 줄이고자 하는 연구가 많이 진행된다. 본 논문에서는 외판원 문제의 최적의 해를 구하는데. 휴리스틱 알고리즘인 최근접 휴리스틱을 이용한다. 물론 수행 시간을 줄이고자 최적화 문제에서 좋은 성능을 보이는 유전 알고리즘 (Genetic Algorithm)으로 얻은 근사해(near optimal)를 초기 분기 함수로 사용하고, 근거리 통신망(Local Area Network)에 기반한 분산 처리 환경에서 여러 프로세서에 분산시켜 병렬성을 살린다.

• Proceedings of the Korean Information Science Society Conference
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• 2005.07a
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• pp.10-12
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• 2005

[$n\timesn$] 불리언 행렬의 집합에서 동치관계를 이용하여 정의된 D-클래스는 개인키나 공개키 암호기술에 사용될 수 있는 가능성을 가지고 있다. 그러나 NP-완전 문제인 계산 복잡도로 인해 D-클래스의 효율적인 계산이 어려워 극히 제한된 크기의 행렬에 대한 D-클래스만이 알려져 있다. D-클래스를 효율적으로 계산하기 위해서는 수식변환, 병렬처리, 순환문 개선 등을 통해 알고리즘을 개선하여야 한다. 본 논문은 D-클래스의 효율적 계산을 위해 공유메모리 기반의 병렬 처리에 적합하도록 수식의 대수적 변환을 이용한 알고리즘의 설계라 실행 결과에 대해 논한다.

• Proceedings of the Korean Information Science Society Conference
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• 2012.06c
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• pp.104-106
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• 2012

다양한 그래프 문제들은 대부분 NP-완전 문제로, 그 중 하나인 독립집합을 구하는 문제 또한 최적의 알고리즘이 존재하지 않는다. 따라서 규모가 큰 대용량 그래프 데이터로 독립집합 문제를 처리하기 위해서는 많은 시간과 비용이 소요된다. 이를 효율적으로 해결하기 위해 분산 환경에서 그래프 처리에 적합한 모델인 Pregel을 이용하여 독립집합 문제를 푼다. 이를 위해 정점 사이의 메시지 전달에 따른 정점 상태 변환 방법을 이용하여 분산 병렬 환경에 알맞은 알고리즘을 제안한다.

• Journal of the Korea Society of Computer and Information
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• v.18 no.9
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• pp.121-129
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• 2013

This paper proposes a linear-time algorithm that has been designed to obtain an accurate solution for Dominating Set (DS) problem, which is known to be NP-complete due to the deficiency of polynomial-time algorithms that successfully derive an accurate solution to it. The proposed algorithm does so by repeatedly assigning vertex v with maximum degree ${\Delta}(G)$among vertices adjacent to the vertex v with minimum degree ${\delta}(G)$ to Minimum Independent DS (MIDS) as its element and removing all the incident edges until no edges remain in the graph. This algorithm finally transforms MIDS into Minimum DS (MDS) and again into Minimum Connected DS (MCDS) so as to obtain the accurate solution to all DS-related problems. When applied to ten different graphs, it has successfully obtained accurate solutions with linear time complexity O(n). It has therefore proven that Dominating Set problem is rather a P-problem.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.18 no.3
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• pp.201-207
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• 2018

There is no known polynomial time algorithm for random-type quadratic assignment problem(RQAP) that is a NP-complete problem. Therefore the heuristic or meta-heuristic approach are solve the approximated solution for the RQAP within polynomial time. This paper suggests polynomial time algorithm for random type quadratic assignment problem (QAP) with time complexity of $O(n^2)$. The proposed algorithm applies one-to-one matching strategy between ascending order of sum of distance for each location and descending order of sum of quantity for each facility. Then, swap the facilities for reflect the correlation of distances of locations and quantities of facilities. For the experimental data, this algorithm, in spite of $O(n^2)$ polynomial time algorithm, can be improve the solution than genetic algorithm a kind of metaheuristic method.

• Journal of the Korea Society of Computer and Information
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• v.19 no.12
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• pp.171-175
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• 2014

Gu$\acute{e}$ret et al. tries to obtain the solution using linear programming with $O(m^4)$ time complexity for cane sugar production problem a kind of bin packing problem that is classified as NP-complete problem. On the other hand, this paper suggests the maximum loss of lot first production greedy rule algorithm with O(mlogm) polynomial time complexity underlying assumption of the polynomial time rule to find the solution is exist. The proposed algorithm sorts the lots of sugar loss slope into descending order. Then, we select the lots for each slot production capacity only, and swap the exhausted life span of lots for lastly selected lots. As a result of experiments, this algorithm reduces the $O(m^4)$ of linear programming to O(mlogm) time complexity. Also, this algorithm better result than linear programming.

• The Journal of the Korea Contents Association
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• v.6 no.2
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• pp.27-33
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• 2006

Boolean matrices are applied to a variety of areas and used successfully in many applications, and there are many researches on boolean matrices. Most researches deal with the multiplication of boolean matrices, but all of them focus on the multiplication of two boolean matrices and very few researches deal with the multiplication between many n$\times$m boolean matrices and all m$\times$k boolean matrices. The paper discusses the existing optimal algorithms for the multiplication of two boolean matrices are not suitable for the multiplication between a n$\times$m boolean matrix and all m$\times$k boolean matrices, establishes a theory that enables the efficient multiplication of a n$\times$m boolean matrix and all m$\times$k boolean matrices, and shows the execution results of a multiplication algorithm designed with this theory.

• Journal of the Korea Society of Computer and Information
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• v.20 no.2
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• pp.63-70
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• 2015

In the absence of a polynomial time algorithm capable of obtaining the exact solutions to it, the domatic number problem (DNP) of dominating set (DS) has been regarded as NP-complete. This paper suggests polynomial-time complexity algorithm about DNP. In this paper, I select a vertex $v_i$ of the maximum degree ${\Delta}(G)$ as an element of a dominating set $D_i,i=1,2,{\cdots},k$, compute $D_{i+1}$ from a simplified graph of $V_{i+1}=V_i{\backslash}D_i$, and verify that $D_i$ is indeed a dominating set through $V{\backslash}D_i=N_G(D_i)$. When applied to 15 various graphs, the proposed algorithm has succeeded in bringing about exact solutions with polynomial-time complexity O(kn). Therefore, the proposed domatic number algorithm shows that the domatic number problem is in fact a P-problem.