• 한국경영과학회지
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• 제28권4호
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• pp.191-198
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• 2003

The generalized knapsack problem or gknap is the combinatorial optimization problem of optimizing a nonnegative linear function over the integral hull of the intersection of a polynomially separable 0-1 polytope and a knapsack constraint. The knapsack, the restricted shortest path, and the constrained spanning tree problem are a partial list of gknap. More interesting1y, all the problem that are known to have a fully polynomial approximation scheme, or FPTAS are gknap. We establish some necessary and sufficient conditions for a gknap to admit an FPTAS. To do so, we recapture the standard scaling and approximate binary search techniques in the framework of gknap. This also enables us to find a weaker sufficient condition than the strong NP-hardness that a gknap does not have an FPTAS. Finally, we apply the conditions to explore the fully polynomial approximability of the constrained spanning problem whose fully polynomial approximability is still open.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2004년도 추계학술대회 및 정기총회
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• pp.225-228
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• 2004

The generalized knapsack problem, or gknap is the combinatorial optimization problem of optimizing a nonnegative linear functional over the integral hull of the intersection of a polynomially separable 0 - 1 polytope and a knapsack constraint. Among many potential applications, the knapsack, the restricted shortest path, and the restricted spanning tree problem are such examples. We prove via the ellipsoid method the equivalence between the fully polynomial approximability and a certain pseudo-polynomial separability of the gknap polytope.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2003년도 추계학술대회 및 정기총회
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• pp.93-96
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• 2003

The generalized knapsack problem, or gknap is the combinatorial optimization problem of optimizing a nonnegative linear functional over the integral hull of the intersection of a polynomially separable 0 - 1 polytope and a knapsack constraint. Among many potential applications, the knapsack, the restricted shortest path, and the restricted spanning tree problem are such examples. We establish some necessary and sufficient conditions for a gknap to admit a fully polynomial approximation scheme, or FPTAS, To do so, we recapture the scaling and approximate binary search techniques in the framework of gknap. This also enables us to find a condition that a gknap does not have an FP-TAS. This condition is more general than the strong NP-hardness.

• 한국ITS학회 논문지
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• 제14권6호
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• pp.60-68
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• 2015

최근 첨단기술의 발전은 교통환경에 커다란 변화를 일으키고 있다. 지능형교통시스템(ITS), 자율주행차량 등은 도로 및 자동차는 물론 운전자까지 정보화, 지능화, 자동화하여 안전하고 효율적인 교통운영에 공헌하고 있다. 본 연구에서는 첨단기술의 도입으로 변화하는 미래 교통환경을 위한 모의실험 모형 설계시 고려해야 하는 사항을 제안하였다. 우선 거시적인 설계 방향으로 현실 유사성, 모형 수용성, 규모 확장성을 제안하고 각각에 대한 구체적 고려사항을 나열하였다. 현실에 유사한 실험을 위하여 정산(calibration) 기능이 중요하며, 통신 특성을 위하여 물리 계층(physical layer) 및 맥 계층(MAC layer)에서 발생하는 현상을 구현하여야 한다. 미래의 새로운 교통환경 실험을 수용하려면 API 등 다른 모형의 추가적인 결합을 위한 인터페이스가 고려되어야 한다. 예측하기 어려운 미래 교통환경을 위한 모의실험 모형은 많은 기능을 내재한 거대한 구성보다는 호환 중심의 설계가 필요하며, 실험 규모 확장을 위하여 H/W와 S/W는 함께 최적화되어야 한다. 본 연구의 결과는 미래 교통환경의 모의실험 모형 설계시 가이드라인으로 활용될 것으로 기대된다.

• Journal of Computing Science and Engineering
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• 제7권2호
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• pp.99-111
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• 2013

Approximating a divergence between two probability distributions from their samples is a fundamental challenge in statistics, information theory, and machine learning. A divergence approximator can be used for various purposes, such as two-sample homogeneity testing, change-point detection, and class-balance estimation. Furthermore, an approximator of a divergence between the joint distribution and the product of marginals can be used for independence testing, which has a wide range of applications, including feature selection and extraction, clustering, object matching, independent component analysis, and causal direction estimation. In this paper, we review recent advances in divergence approximation. Our emphasis is that directly approximating the divergence without estimating probability distributions is more sensible than a naive two-step approach of first estimating probability distributions and then approximating the divergence. Furthermore, despite the overwhelming popularity of the Kullback-Leibler divergence as a divergence measure, we argue that alternatives such as the Pearson divergence, the relative Pearson divergence, and the $L^2$-distance are more useful in practice because of their computationally efficient approximability, high numerical stability, and superior robustness against outliers.