• 제목/요약/키워드: NP-completeness

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Release와 Processing time이 투입자원에 종속적인 단일설비 일정계획문제의 Strong NP-completeness 분석 (Strong NP-completeness of Single Machine Scheduling with Resource Dependent Release Times and Processing Times)

  • 이익선
    • 경영과학
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    • 제31권2호
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    • pp.65-70
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    • 2014
  • This paper considers a single machine scheduling problem to determine release and processing times where both the release times and processing times are linearly decreasing functions of resources. The objective is to minimize the sum of the associated resource consumption cost and scheduling cost including makespan, sum of completion times, maximum lateness, or sum of lateness. This paper proves that the scheduling problem is NP-hard in the strong sense even if the release times are constant.

Minimum Energy Cooperative Path Routing in All-Wireless Networks: NP-Completeness and Heuristic Algorithms

  • Li, Fulu;Wu, Kui;Lippman, Andrew
    • Journal of Communications and Networks
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    • 제10권2호
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    • pp.204-212
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    • 2008
  • We study the routing problem in all-wireless networks based on cooperative transmissions. We model the minimum-energy cooperative path (MECP) problem and prove that this problem is NP-complete. We hence design an approximation algorithm called cooperative shortest path (CSP) algorithm that uses Dijkstra's algorithm as the basic building block and utilizes cooperative transmissions in the relaxation procedure. Compared with traditional non-cooperative shortest path algorithms, the CSP algorithm can achieve a higher energy saving and better balanced energy consumption among network nodes, especially when the network is in large scale. The nice features lead to a unique, scalable routing scheme that changes the high network density from the curse of congestion to the blessing of cooperative transmissions.

COMPLEXITY OF THE SCHEDULING LANGUAGE RSV

  • KIM POK-SON;KUTZNER ARNE;PARK TAEHOON
    • Journal of applied mathematics & informatics
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    • 제20권1_2호
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    • pp.181-195
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    • 2006
  • 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.

완전 피복 문제의 원소 수 기반 알고리즘 (Algorithm Based on Cardinality Number of Exact Cover Problem)

  • 이상운
    • 한국인터넷방송통신학회논문지
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    • 제23권2호
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    • pp.185-191
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    • 2023
  • 본 논문은 지금까지 NP-완전 문제로 다항시간 알고리즘이 존재하지 않는 완전피복 문제에 대해 선형시간으로 해를 구할 수 있는 알고리즘을 제안하였다. 제안된 알고리즘은 "행과 열에는 동일한 값이 존재하면 안된다"는 완전피복문제의 특징을 이용하였다. 이를 위해 먼저 최소 원소 개수를 가진 부분집합을 선택하고 선택된 부분집합의 원소를 가진 부분집합을 삭제하였다. 남은 부분집합들을 대상으로 반복적으로 수행하면 해를 구한다. 만약, 해를 구하지 못하면 최대 원소 개수를 가진 부분집합을 선택하여 동일한 과정을 수행하였다. 제안된 알고리즘은 일반적인 완전피복 문제의 해를 쉽게 구하였다. 추가로, 완전피복 문제를 보다 일반화한 N-퀸 문제를 대상으로 제안된 알고리즘을 적용할 수 있음을 보였다. 결국, 제안된 완전피복 알고리즘은 완전피복 문제에 대해 P-문제임을 증명하였다.

거리반경기반 대표문자열 문제의 NP-완전 (The Consensus String Problem based on Radius is NP-complete)

  • 나중채;심정섭
    • 한국정보과학회논문지:시스템및이론
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    • 제36권3호
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    • pp.135-139
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    • 2009
  • 여러 문자열들을 비교하여 유사성 또는 거리(오차)를 계산하는 문제는 패턴매칭, 웹검색 바이오인포매틱스, 컴퓨터 보안 등 다양한 응용 분야와의 연관성으로 인해 활발히 연구되어 왔다. 주어진 문자열 집합 내의 여러 문자열들의 거리를 비교하기 위해 주어진 집합 내의 모든 문자열들을 대표하는 한 문자열(대표문자열)을 찾는 방법이 있다. 대표문자열 방법은 주어진 문자열 집합과 가장 유사한 한 문자열을 찾는 방법으로 주로 이용되는 목적함수는 거리반경과 거리합이 있다. 거리반경은 집합 내의 문자열들과 특정 문자열과의 거리들의 최대값으로 정의되며, 모든 문자열들 중에서 최소의 거리반경을 만드는 문자열을 주어진 문자열 집합에 대한 거리반경기반 대표문자열이라 한다. 거리합은 집합 내의 문자열들과 특정 문자열과의 거리들의 합으로 정의되며, 모든 문자열들 중에서 최소의 거리합을 만드는 문자열을 주어진 문자열집합에 대한 거리합기반 대표문자열이라 한다. 본 논문에서는 메트릭 거리함수에 대해 거리반경기반 대표문자열 문제가 NP-완전임을 증명한다.

다목적 셀 형성을 위한 유전알고리즘 (A Genetic Algorithm for A Cell Formation with Multiple Objectives)

  • 이준수;정병호
    • 산업경영시스템학회지
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    • 제26권4호
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    • pp.31-41
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    • 2003
  • This paper deals with a cell formation problem for a set of m-machines and n-processing parts. Generally, a cell formation problem is known as NP-completeness. Hence the cell formation problem with multiple objectives is more difficult than single objective problem. The paper considers multiple objectives; minimize number of intercell movements, minimize intracell workload variation and minimize intercell workload variation. We propose a multiple objective genetic algorithms(MOGA) resolving the mentioned three objectives. The MOGA procedure adopted Pareto optimal solution for selection method for next generation and the concept of Euclidean distance from the ideal and negative ideal solution for fitness test of a individual. As we consider several weights, decision maker will be reflected his consideration by adjusting high weights for important objective. A numerical example is given for a comparative analysis with the results of other research.

라그랑지안 기반의 휴리스틱 기법을 이용한 셀룰러 모바일 네트워크의 설계 (Designing Cellular Mobile Network Using Lagrangian Based Heuristic)

  • 홍정만;이종협
    • 대한산업공학회지
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    • 제37권1호
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    • pp.19-29
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    • 2011
  • Cellular network is comprised of several base stations which serve cellular shaped service area and each base station (BS) is connected to the mobile switching center (MSC). In this paper, the configuration modeling and algorithm of a cellular mobile network with the aim of minimizing the overall cost of operation (handover) and network installation cost (cabling cost and installing cost of mobile switching center) are considered. Handover and cabling cost is one of the key considerations in designing cellular telecommunication networks. For real-world applications, this configuration study covers in an integrated framework for two major decisions: locating MSC and assigning BS to MSC. The problem is expressed in an integer programming model and a heuristic algorithm based on Lagrangian relaxation is proposed to resolve the problem. Searching for the optimum solution through exact algorithm to this problem appears to be unrealistic considering the large scale nature and NP-Completeness of the problem. The suggested algorithm computes both the bound for the objective value of the problem and the feasible solution for the problem. A Lagrangian heuristics is developed to find the feasible solution. Numerical tests are performed for the effectiveness and efficiency of the proposed heuristic algorithm. Computational experiments show that the performance of the proposed heuristics is satisfactory in the quality of the generated solution.