Fractional b-matching 문제에 대한 그래프 단체법에 관한 연구

학위논문(석사)--서울대학교 대학원 :산업공학과,1997.Maste

Approximation algorithms for the constrained network optimization

학위논문(박사)--서울대학교 대학원 :산업공학과,2004.Docto

About fully Polynomial Approximability of the Generalized Knapsack Problem

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 interestingly, 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.이 논문은 2000년도 중앙대학교 학술연구비 지원에 의한 것임

A Simple Fully Polynomial Approximation Scheme for the Restricted Shortest Path Problem

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.이 연구는 1999년도 한국학술진흥재단의 연구비에 의하여 지원되었음(KRF-99-041-E00125