한국경영과학회:학술대회논문집 (Proceedings of the Korean Operations and Management Science Society Conference)
- 한국경영과학회 2003년도 추계학술대회 및 정기총회
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- Pages.93-96
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- 2003
About fully polynomial approximability of the generalized knapsack problem
- Hong, Sung-Pil (School of Business, Chung-Ang University) ;
- Park, Bum-Hwan (Industrial Engineering, Seoul National University)
- 발행 : 2003.11.01
초록
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.
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