• Journal of KIISE:Computer Systems and Theory
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• v.31 no.10
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• pp.562-574
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• 2004

We address the problem of energy-optimal voltage scheduling for fixed-priority hard real-time systems. First, we prove that the problem is NP-hard. Then, we present a fully polynomial time approximation scheme (FPTAS) for the problem. for any $\varepsilon$>0, the proposed approximation scheme computes a voltage schedule whose energy consumption is at most (1+$\varepsilon$) times that of the optimal voltage schedule. Furthermore, the running time of the proposed approximation scheme is bounded by a polynomial function of the number of input jobs and 1/$\varepsilon$. Experimental results show that the approximation scheme finds more efficient voltage schedules faster than the best existing heuristic.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.48 no.5
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• pp.64-73
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• 2011

The problem of Euclidean minimum spanning tree (EMST) is to connect given nodes in a plane with minimum cost. There are many algorithms for the polynomial time problem as EMST. However, for numerous nodes, the algorithms consume an enormous amount of time to find an optimal solution. In this paper, an approximation scheme using a polynomial time approximation scheme (PTAS) algorithm with dividing and parallel processing for the problem is suggested. This scheme enables to construct a large, approximate EMST within a short duration. Although initially devised for the non-polynomial problem, we employ naive PTAS to construct a vast EMST with dynamic programming. In an experiment, the approximate EMST constructed by the proposed scheme with 15,000 input terminal nodes and 16 partition cells shows 89% and 99% saving in execution time for the serial processing and parallel processing methods, respectively. Therefore, our scheme can be applied to obtain an approximate EMST quickly for numerous input terminal nodes.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.4
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• pp.379-383
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• 2001

The restricted shortest path problem is known to be weakly NP-hard and solvable in pseudo-polynomial time. Four fully polynomial approximation schemes (FPAS) are available in the literature, and most of these are based on pseudo-polynomial algorithms. In this paper, we propose a new FPAS that can be easily derived from a combination of a set of standard techniques. Although the complexity of the suggested algorithm is not as good as the fastest one available in the literature, it is practical in the sense that it does not rely on the bound tightening phase based on approximate binary search as in Hassin's fastest algorithm. In addition, we provide a review of standard techniques of existing works as a useful reference.

• Journal of Korea Spatial Information System Society
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• v.7 no.2 s.14
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• pp.57-66
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• 2005

The Interconnecting Highways problem is an abstract of many practical Layout Design problems in the areas of VLSI design, the optical and wired network design, and the planning for the road constructions. For the road constructions, the shortest-length road layouts that interconnect existing positions will provide many more economic benefits than others. That is, finding new road layouts to interconnect existing roads and cities over a wide area is an important issue. This paper addresses an approximation scheme that finds near optimal road layouts for the Interconnecting Highways problem which is NP-hard. As long as computational resources are provided, the near optimality can be acquired asymptotically. This implies that the result of the scheme can be regarded as the optimal solution for the problem in practice. While other approximation schemes can be made for the problem, this proposed scheme provides a big merit that the algorithm designed by this scheme fits well to given problem instances.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.3C
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• pp.248-256
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• 2003

Space-time coding was designed for an efficient transmit diversity technique to improve performance of wireless communication. For the transmit diversity using space-time coding, the receiver requires to estimate channel parameters corresponding to each transmit antennas. In this paper, we propose an efficient channel estimation scheme based on trigonometric polynomial approximation in OFDM systems with transmit diversity using space-time coding. The proposed scheme is more efficient than the conventional scheme in terms of the computational complexity. For QAM modulation, when the size of FFH is 128, the conventional scheme with significant tap caching of 7 requires 9852 complex multiplications for TU, HT and BU channels. But the proposed scheme requires 2560, 7680 and 3584 complex multiplications for TU, HT and BU channels, respectively. Especially, for channels with smaller Doppler frequency and delay spreads, the proposed scheme has the improved BER performance and complexity. In addition, we evaluate the performance of maximum delay spread estimation in unknown channel. The performance of the proposed scheme is investigated by computer simulation in various multi-path fading environments.

• Journal of the Korea Society of Computer and Information
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• v.19 no.6
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• pp.71-80
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• 2014

Employing PTAS to building minimum spanning tree for a large number of equal distribution input terminal nodes can be a effective way in execution time. But applying PTAS to building minimum spanning tree for tremendous unequal distribution node may lead to performance degradation. In this paper, a partial PTAS reflecting the scheme into specific node dense area is presented. In the environment where 90% of 50,000 input terminal nodes stand close together in specific area, approximate minimum spanning tree by our proposed scheme can show about 88.49% execution time less and 0.86%tree length less than by existing PTAS, and about 87.57%execution time less and 1.18% tree length more than by Prim's naive scheme. Therefore our scheme can go well to many useful applications where a multitude of nodes gathered around specific area should be connected efficiently as soon as possible.

• Proceedings of the Korea Multimedia Society Conference
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• 2012.05a
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• pp.419-421
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• 2012

멀티미디어 통신을 희망하는 수많은 노드들이 비 균등하게 분포되어 있는 환경에서 PTAS 기법을 사용하여 효과적으로 통신가능하게 하는 통신 네트워크 시스템의 구축이 가능하게 하는 방법을 제안한다.

• Journal of the Korea Society of Computer and Information
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• v.16 no.11
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• pp.153-161
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• 2011

As the problem of GOSST building belongs to NP compete domain, heuristics for the problem ask for immense amount execution time and computations in large scale inputs. In this paper, we propose an efficient mechanism for GOSST construction using space locality PTAS. For 40,000 input nodes with maximum weight 100, the proposed space locality PTAS GOSST with 16 unit areas can reduce about 4.00% of connection cost and 89.26% of execution time less than weighted minimum spanning tree method. Though the proposed method increases 0.03% of connection cost more, but cuts down 96.39% of execution time less than approximate GOSST method (SGOSST) without PTAS. Therefore the proposed space locality PTAS GOSST mechanism can work moderately well to many useful applications where a greate number of weighted inputs should be connected in short time with approximate minimum connection cost.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.05a
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• pp.145-150
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• 2003

The parallel machine scheduling problem or assigning n jobs on m identical machines with the objective of minimizing makespan is considered. In this note, we apply the PTAS (Polynomial Time Approximation Scheme) or Hochbaum and Shmoys to our problem and show that it is still a PTAS for our problem.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.47 no.5
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• pp.25-34
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• 2010

By introducing additional nodes called Steiner points, the problem of Steiner Minimum Tree whose length can be shorter than Minimum Spanning Tree and which connects all input terminal nodes belongs to Non-Polynomial Complete domain. Though diverse heuristic methods can be applied to the problem, most of them may meet serious pains in computing and waiting for a solution of the problem with numerous input nodes. For numerous input nodes, an efficient PTAS approximation method producing candidate unit steiner trees with portals in most bottom layer, merging them hierarchically to construct their parent steiner trees in upper layer and building swiftly final approximation Steiner tree in most top layer is suggested in this paper. The experiment with 16,000 input nodes and designed 16 unit areas in most bottom layer shows 85.4% execution time improvement in serial processing and 98.9% in parallel processing comparing with pure Steiner heuristic method, though 0.24% overhead of tree length. Therefore, the suggested PTAS Steiner tree method can have a wide range applications to build a large scale approximation Steiner tree quickly.