• 대한산업공학회지
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• 제27권4호
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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.

• 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.

• 한국정보과학회논문지:시스템및이론
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• 제31권10호
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• pp.562-574
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• 2004

본 논문에서는 고정 우선순위 경성 실시간 시스템에 대한 에너지 측면에서의 최적의 전압 스케줄링 문제를 고려한다. 먼저, 이 문제가 NP-hard임을 증명한다. 다음으로 이 문제에 대한 fully polynomial time approximation scheme(FPTAS)을 제시한다 제안한 FPTAS는 주어진 임의의 $\varepsilon$>0에 대해 에너지 소모량이 최적의 전압 스케줄에 비해 (1＋$\varepsilon$)배 이내에 있는 전압 스케줄을 문제의 입력의 크기와 1/$\varepsilon$의 다항함수 이내의 시간에 계산해준다. 실험 결과, 제안된 FPTAS는 기존의 휴리스틱에 비해 더 효율적인 전압 스케줄을 더 빠른 시간에 찾아주었다.

• 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.