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ICT활용을 통한 수학교육의 효율성 향상과 활용 현황에 관한 조사 및 연구
대진옥,김복선 국민대학교 2003 기초과학연구소 논문집 Vol.22 No.-
The ICT utility education has come to representative topic in our educational circles for several years. We think the method of mathematics education by means of the ICT utility could fill the blank of present educational method. The purpose of this study is to investigate how much the ICT(Information & Communication Technology) utility instruction is utilized in the mathematics education and what effect relations with the school achievement it takes. Further we investigate which parts of present ICT utility instruction should be improved in the future.
COMPLEXITY OF THE SCHEDULING LANGUAGE RSV
KIM, POK-SON,KUTZNER, ARNE,PARK, TAEHOON 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.20 No.1
Resource-constrained project scheduling problems with variant processes can be represented and solved using a logic-based terminological language called RSV (resource constrained project scheduling with variant processes). We consider three different variants for formalizing the RSV-scheduling problem, the optimizing variant, the number variant and the decision variant. Using the decision variant we show that the RSV- problem is NP-complete. Further we show that the optimizing variant (or number variant) of the RSV-problem is computable in polynomial time iff. the decision variant is computable in polynomial time.
Pok-Son Kim(김복선) 한국지능시스템학회 2014 한국지능시스템학회논문지 Vol.24 No.2
The logic-based scheduling language RCPSV may be used to model resource-constrained project scheduling problems with variants for minimizing the project completion time. A diagram-based, nonredundant enumeration algorithm for the RCPSV-problem is proposed and the correctness of the algorithm is proved.
NP-Completeness of the Logic-Based Scheduling Language RS
Kim, Pok-Son,Kutzner, Arne,Park, Taehoon 국민대학교 2003 기초과학연구소 논문집 Vol.22 No.-
RSV 언어의 부분클래스에 해당하는 언어 RS 를 정의하고, RS 문제해결에 있어서 계산시간과 관련한 복잡도에 대해 연구하는것이 이 논문의 목적이다. RSV에서 세가지 구조적 연산 seq, xor 그리고 pll 이 이용되는 반면 RS에서 단지 두 연산 seq 그리고 pll이 문제 표현을 위한 구조적 연산으로 이용되며, 우리는 이 논문에서 RS-문제가 클래스 NP에 속하며, NP-완전문제에 해당하는 knapsack-문제로 RS-문제를 다항식시간 귀착가능 (polynomial reducible) 함으로 보이므로 RS-문제가 NP-완전함을 증명해 보인다. The language RS, a subclass of the scheduling language RSV (resource constrained project scheduling with variant processes), involves the determining of the starting times for ground activities of a project satisfying precedence and resource constraints, in order to minimize the total project duration. In RS only two structural symbols (operators) `seq’ and ‘p11’, instead of three structural symbols (operators) `seq’, `xor’ and ‘pll’ of RSV, are used to construct activity-terms representing scheduling problems. The purpose of this paper is to investigate which time complexity is needed for solving the problem RS. We show the problem RS belongs to the problem class NP and the well-known NP-complete knapsack problem is polynomial reducible to the problem RS. So the problem RS is NP-complete.
Kim, Pok-Son,Park, Taehoon 국민대학교 2002 기초과학연구소 논문집 Vol.21 No.-
There are three different variants for formalizing theNP-complete RSV-scheduling problem. These are the optimizing variant, the number variant and the decision variant. In general, based on the decision variant of a problem the NP-completeness is showed. In this paper we prove that the NP-Completeness of the RSV-problem may be transfered from the decision variant to the optimizing and the number variant.
Complexity of the Symmerge Algorithm
Pok-Son Kim(김복선) 한국지능시스템학회 2008 한국지능시스템학회논문지 Vol.18 No.2
m≤n을 만족하는 m과 n을 두 입력수열이라고 했을 때 Symmerge는 비교횟수와 관련해 복잡도 O(mlog n/m)를 필요로 하는 stable minimum storage 머징 알고리즘이다. 그러므로 비교횟수와 관련된 머징의 점근적 하계 Ω(mlog n/m)에 의해 Symmerge 알고리즘은 최적 알고리즘에 해당함을 알 수 있다. Symmerge는 두 입력수열의 분할 (partition)과 로테이션 (rotation)을 통해 얻어지는 수열들에 알고리즘의 재귀적 콜 (recursive call)이 적용되는 divide 와 conquer 기술을 이용한다. 이로 인해 수열들이 반복해서 분할과 로테이션 되는데 특히 재귀의 깊이가 m-1 가 되는 경우에 있어서 두 입력수열의 길이의 관계를 알아보고자 한다. Symmerge is a stable minimum storage merging algorithm that needs O(mlog n/m) element comparisons, where m and n are the sizes of the input sequences with m≤n. Hence, according to the lower bound for merging, the algorithm is asymptotically optimal regarding the number of comparisons. The Symmerge algorithm is based on the standard recursive technique of "divide and conquer". The objective of this paper is to consider the relationship between m and n for the degenerated case where the recursion depth reaches m-1.