일반배낭문제의 완전다항시간근사해법군의 존재조건

About fully Polynomial Approximability of the Generalized Knapsack Problem

  • 홍성필 (중앙대학교 사회과학대학 상경학부) ;
  • 박범환 (서울대학교 대학원 산업공학과)
  • 발행 : 2003.12.01

초록

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.

키워드

참고문헌

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