Recall that the approximation ratio for an approximation algorithm is a measure to evaluate the approximation performance of the algorithm. The closer the ratio to 1 the better the approximation performance of the algorithm. It is notable that there is a class of NP-hard optimization problems, most originating from scheduling problems, for which there are polynomial time approximation algorithm...

In this paper, we consider computational methods for optimizing a multivariate inhomogeneous polynomial function over a compact set. The focus is on the design and analysis of polynomial-time approximation algorithms. The references on approximation algorithms for inhomogeneous polynomial optimization problems are extremely scarce in the literature. To the best of our knowledge, the only result...

In this paper, we set up a framework to study approximation of manipulation, control, and bribery in elections. We show existence of approximation algorithms (even fully polynomial-time approximation schemes) as well as obtain inapproximability results. In particular, we show that a large subclass of scoring protocols admits fully polynomial-time approximation schemes for the coalitional weight...

We show the existence of a fully polynomial-time approximation scheme (FPTAS) for the problem of maximizing a non-negative polynomial over mixedinteger sets in convex polytopes, when the number of variables is fixed. Moreover, using a weaker notion of approximation, we show the existence of a fully polynomial-time approximation scheme for the problem of maximizing or minimizing an arbitrary pol...

A fully implementable filtered polynomial approximation on spherical shells is considered. The method proposed is a quadrature-based version of a filtered polynomial approximation. The radial direction and the angular direction of the shells are treated separately with constructive filtered polynomial approximation. The approximation error with respect to the supremum norm is shown to decay alg...

We give sufficient conditions for deriving moderately exponential and/or parameterized time approximation schemata (i.e., algorithms achieving ratios 1± , for arbitrarily small ) for broad classes of combinatorial optimization problems via a well-known technique widely used for deriving exact algorithms, namely the branching tree pruning. Mathematics Subject Classification. 68W25, 05C85, 68Q25....

We present the software package WAM, written in Matlab, that generates Weakly Admissible Meshes and Discrete Extremal Sets of Fekete and Leja type, for 2d and 3d polynomial least squares and interpolation on compact sets with various geometries. Possible applications range from data fitting to high-order methods for PDEs.