• 한국경영과학회지
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• 제36권2호
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• pp.43-50
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• 2011

We consider the separation problem of the rank-1 Chvatal-Gomory (C-G) inequalities for the 0-1 knapsack problem with the knapsack capacity defined by an additional binary variable, which we call the fixed-charge 0-1 knapsack problem. We analyze the structural properties of the optimal solutions to the separation problem and show that the separation problem can be solved in pseudo-polynomial time. By using the result, we also show that the existence of a pseudo-polynomial time algorithm for the separation problem of the rank-1 C-G inequalities of the ordinary 0-1 knapsack problem.

• 정보보호학회논문지
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• 제1권1호
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• pp.16-28
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• 1991

Knapsack 암호체계는 NP-Complete 인 Knapsack 문제에 기초한 공개키 암호체계이다. 이러한 암호체계의 안정성에 관하여서는 그동안 많은 논란이 있어 왔다. 쉬운 Knapsack 문제를 모듈라연산으로 숨기는 거의 모든Knapsack 암호체계가 계속하여 개발되어 왔다.특히 Bose-Chowla 정리에 근거하여 모듈라 연산을 사용하지 않는 Chor_Rivest knapsack 암호체계는 기존의 모든 암호분석 방법에 대하여 안전한 것으로 알려져 있다. 본 연구에서는 Knapsack 문제를 정수계획법 문제로 변환하고 이를 이완하여 해를 구함으로써 Knapsack 문제의 부분해를 구할 수 있음을 보인다. 이는 일반적인 Knapsack 암호체계는 구현상의 효율성이 제고된 안전한 Knapsack 공개키 암호체계를 제시하고자 한다.

• Management Science and Financial Engineering
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• 제14권1호
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• pp.91-96
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• 2008

Robust knapsack problem appears when dealing with data uncertainty on the knapsack constraint. This note presents a generalization of the cover inequality for the problem with its lifting procedure. Specifically, we show that the lifting can be done in a polynomial time as in the usual knapsack problem. The results can serve as a building block in devising an efficient branch-and-cut algorithm for the general robust (0, 1) IP problem.

• 융합보안논문지
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• 제14권7호
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• pp.59-64
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• 2014

이 논문에서는 고정된 개수를 가진 bin들을 이용하여 실행 복잡도가 $p(n){\cdot}2^{O(\sqrt{n})}$인 알고리즘을 제시한다, 여기서 x는 (5)n개의 객체들에 대한 리스트의 길이에 대한 총 비트 수를 나타낸다. 이러한 방법은 수치적 크기나 비중의 합의 리스트를 이용하는 여러 가지 최적화 알고리즘이나 결정 문제등에 적용할 수 있다. 이 논문에서 제시한 알고리즘은 의사-다항식(pseudo-polynomial) 시간을 갖는 NP-Complete의 많은 문제들을 결정적인 서브-지수 시간에 해결할 수 있은 가능성을 제시한다. 여기서 제시한 알고리즘을 이용하여 생명공학의 유전자 분석에 적용하려고 한다.

• 대한산업공학회지
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• 제38권2호
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• pp.74-79
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• 2012

An efficient separation heuristic for the rank-1 Chvatal-Gomory cuts for the binary knapsack problem is proposed. The proposed heuristic is based on the decomposition property of the separation problem for the fixedcharge 0-1 knapsack problem characterized by Park and Lee [14]. Computational tests on the benchmark instances of the generalized assignment problem show that the proposed heuristic procedure can generate strong rank-1 C-G cuts more efficiently than the exact rank-1 C-G cut separation and the exact knapsack facet generation.

• 산업경영시스템학회지
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• 제19권40호
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• pp.137-142
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• 1996

An algorithm for solving the cardinality constrained linear programming knapsack problem is presented. The algorithm has a convenient structure for a branch-and-bound approach to the integer version, especially to the 0-1 collapsing knapsack problem. A numerical example is given.

• 한국경영과학회지
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• 제31권1호
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• pp.55-71
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• 2006

We perform a computational study on 0-1 knapsack problems generated under explicit correlation induction. A total of 2000 100-variable test problems are solved. We use two solution methods: (1) a well known heuristic and (2) a representative branch and bound type algorithm. Two different performance measures are considered: (1) the number of nodes needed to find an optimal solution and (2) the relative error of the heuristic solution. We also examine the effect of different joint probability mass functions (pmfs) for the coefficient values on the performance of the solution procedure.

• 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.

• 융합신호처리학회 학술대회논문집
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• 한국신호처리시스템학회 2000년도 하계종합학술대회논문집
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• pp.341-344
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• 2000

The 0-1 knapsack processor performing dynamic programming is designed and implemented on a programmable logic device. Three types of a processor, each with different behavioral models, are presented, and the operation of a processor of each type is verified with an instance of the 0-1 knapsack problem.