The purpose of this paper is to mainly prove the following theorem: for every polynomial time algorithm running in time T (n) and guaranteeing standard-approximation ratio ρ for bin-packing, there exists an algorithm running in time O(nT (n)) and achieving differentialapproximation ratio 2 − ρ for BP. This theorem has two main impacts. The first one is “operational”, deriving a polynomial time ...

The purpose of this paper is to mainly prove the following theorem: for every polynomial time algorithm running in time T (n) and guaranteeing standard-approximation ratio ρ for bin-packing, there exists an algorithm running in time O(nT (n)) and achieving differentialapproximation ratio 2 − ρ for BP. This theorem has two main impacts. The first one is “operational”, deriving a polynomial time ...

Pseudoknotted RNA structure prediction is an important problem in bioinformatics. Existing polynomial time algorithms have no performance guarantee or can handle only limited types of pseudoknots. In this paper for the general problem of pseudoknotted RNA structure prediction, maximum weighted stacking problem is presented based on stacking actions, and its polynomial time approximation algorit...

In this paper, we consider approximation algorithms for optimizing a generic multi-variate homogeneous polynomial function, subject to homogeneous quadratic constraints. Such optimization models have wide applications, e.g., in signal processing, magnetic resonance imaging (MRI), data training, approximation theory, and portfolio selection. Since polynomial functions are nonconvex in general, t...

The theoretical and experimental background for the approximation of "real-world" functions is reviewed to motivate the use of piecewise polynomial approximations. It is possible in practice ~o achieve the results suggested by the theory for piecewise polynomials. A convergent adaptive algorithm is outlined which effectively and efficiently computes smooth piecewise polynomial approxImations to...