• Title, Summary, Keyword: NP-hard

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An Approximation Scheme For A Geometrical NP-Hard Problem (기하학적 NP-hard 문제에 대한 근사 접근법)

  • Kim, Joon-Mo
    • Journal of the Institute of Electronics Engineers of Korea TC
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    • v.44 no.8
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    • pp.62-67
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    • 2007
  • In some wireless sensor networks, the sensor nodes are required to be located sparsely at designated positions over a wide area, introducing the problem of adding minimum number of relay nodes to interconnect the sensor nodes. The problem finds its form in literature: the Minimum number of Steiner Points. Since it is known to be NP-hard, this paper proposes an approximation scheme to estimate the minimum number of relay nodes through the properties of the abstract from. Reducing the number of nodes in a sensor network, the amount of data exchange over the net will be far decreased.

Interconnection Problem among the Dense Areas of Nodes in Sensor Networks (센서네트워크 상의 노드 밀집지역 간 상호연결을 위한 문제)

  • Kim, Joon-Mo
    • Journal of the Institute of Electronics Engineers of Korea TC
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    • v.48 no.2
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    • pp.6-13
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    • 2011
  • This paper deals with the interconnection problem in ad-hoc networks or sensor networks, where relay nodes are deployed additionally to form connections between given nodes. This problem can be reduced to a NP-hard problem. The nodes of the networks, by applications or geographic factors, can be deployed densely in some areas while sparsely in others. For such a case one can make an approximation scheme, which gives shorter execution time, for the additional node deployments by ignoring the interconnections inside the dense area of nodes. However, the case is still a NP-hard, so it is proper to establish a polynomial time approximation scheme (PTAS) by implementing a dynamic programming. The analysis can be made possible by an elaboration on making the definition of the objective function. The objective function should be defined to be able to deal with the requirement incurred by the substitution of the dense area with its abstraction.

Computing a Minimum-Dilation Spanning Tree is NP-hard (최소-Dilation 신장 트리 찾기의 NP-hard 증명)

  • Cheong, Otfried;Haverkort, Herman;Lee, Mi-Ra
    • Proceedings of the Korean Information Science Society Conference
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    • pp.494-499
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    • 2006
  • Given a set S of n points in the plane, a minimum-dilation spanning tree of S is a tree with vertex set S of smallest possible dilation. We show that given a set S of n points and a dilation $\delta$ > 1, it is NP-hard to determine whether a spanning tree of S with dilation at most $\delta$ exists.

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AN APPROXIMATION SCHEME FOR A GEOMETRICAL NP-HARD PROBLEM

  • Kim, Joon-Mo
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.11 no.4
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    • pp.1-8
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    • 2007
  • In some wireless sensor networks, the sensor nodes are required to be located sparsely at designated positions over a wide area, introducing the problem of adding minimum number of relay nodes to interconnect the sensor nodes. The problem finds its a bstract form in literature: the Minimum number of Steiner Points. Since it is known to be NP-hard, this paper proposes an approximation scheme to estimate the minimum number of relay nodes through the properties of the abstract form. Note that by reducing the numb er of nodes in a sensor network, the amount of data exchange over the net will be far decreased.

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An analysis on Trailer and Tractor Problem (TTP) (트레일러-트렉터문제에 대한 연구)

  • Han, Yun-Taek;Jang, Su-Yeong
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • pp.284-287
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    • 2006
  • We consider the transportation problem of optimizing the use of trailers and tractors. Several variants with fixed loading and unloading time are discussed. We show that the variant requiring on-time delivery can be solved in polynomial time, whereas the other variant requiring time-window delivery is NP-hard. We also discuss that if the number of loading and unloading operations assigned to each trailer or tractor is limited, even the variant requiring on-time delivery becomes NP-hard.

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Inapproximability of the Max-cut Problem with Negative Weights

  • Hong, Sung-Pil
    • Management Science and Financial Engineering
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    • v.14 no.1
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    • pp.87-90
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    • 2008
  • We show that when a max-cut problem is allowed native-weight edges, to decide if the problem has a cut of a positive weight is NP-hard. This implies that there is no polynomial time algorithm which guarantees a cut whose objective value is no less than $1/p(<I>)$ times the optimum for any polynomially computable polynomial p, where denotes the encoding length of an instance I.

Gel Image Matching Using Hopfield Neural Network (홉필드 신경망을 이용한 젤 영상 정합)

  • Ankhbayar Yukhuu;Hwang Suk-Hyung;Hwang Young-Sup
    • The KIPS Transactions:PartB
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    • v.13B no.3
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    • pp.323-328
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    • 2006
  • Proteins in a cell appear as spots in a two dimensional gel image which is used in protein analysis. The spots from the same protein are in near position when comparing two gel images. Finding out the different proteins between a normal tissue and a cancer one is important information in drug development. Automatic matching of gel images is difficult because they are made from biological experimental processes. This matching problem is known to be NP-hard. Neural networks are usually used to solve such NP-hard problems. Hopfield neural network is selected since it is appropriate to solve the gel matching. An energy function with location and distance parameters is defined. The two spots which make the energy function minimum are matching spots and they came from the same protein. The energy function is designed to reflect the topology of spots by examining not only the given spot but also neighborhood spots.

A Tabu Search Algorithm for the Network Diversion Problem (네트워크 전환문제에 대한 타부 탐색 해법)

  • 양희원;박성수
    • Journal of the military operations research society of Korea
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    • v.30 no.1
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    • pp.30-47
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    • 2004
  • This research considers a Network Diversion Problem (NDP) in the directed graph, which is to identify a minimum cost set of links to cut so that any communication paths from a designated source node to a destination node must include at least one link from a specified set of arcs which is called the diversion arcs. We identify a redundant constraint from an earlier formulation. The problem is known to be NP-hard, however a detailed proof has not been given. We provide the proof of the NP-hardness of this problem. We develop a tabu search algorithm that includes a preprocessing procedure with two steps for removing diversion arcs as well as reducing the problem size. Computational results of the algorithm on instances of general graphs and grid graphs are reported.

Multi-Parameter Operation Method for Robust Disparity Plane (강건한 시차 평면을 위한 다중 파라미터 연산 기법)

  • Kim, Hyun-Jung;Weon, Il-Yong;Lee, Chang-Hun
    • KIPS Transactions on Software and Data Engineering
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    • v.4 no.5
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    • pp.241-246
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    • 2015
  • Although many different methods have been used to solve stereo correspondent problems, the deviation of accuracy is too big. Among those many methods, the one that uses segmentation information of input image has received high attention in academic field since it is very close to vision recognition. In this thesis, the existing method of acquiring a single value by using the segment information and initial disparity value was viewed in NP-hard problem to propose a new method. In order to verify the validity of the proposed method, well-known data were used for experiment and the resulted data was analyzed. Although there were some disadvantages in the time aspect, it showed somewhat useful results in the accuracy aspect.

Genetic Algorithm Using-Floating Point Representation for Steiner Tree (스타이너 트리를 구하기 위한 부동소수점 표현을 이용한 유전자 알고리즘)

  • 김채주;성길영;우종호
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.8 no.5
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    • pp.1089-1095
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    • 2004
  • The genetic algorithms have been used to take a near optimal solution because The generation of the optimal Steiner tree from a given network is NP-hard problem,. The chromosomes in genetic algorithm are represented with the floating point representation instead of the existing binary string for solving this problem. A spanning tree was obtained from a given network using Prim's algorithm. Then, the new Steiner point was computed using genetic algorithm with the chromosomes in the floating point representation, and it was added to the tree for approaching the result. After repeating these evolving steps, the near optimal Steiner tree was obtained. Using this method, the tree is quickly and exactly approached to the near optimal Steiner tree compared with the existing genetic algorithms using binary string.