Given an integer function f , the problem is to find its best uniform approximation from a set K of integervalued bounded functions. Under certain conditions on K , the best extremal (maximal or minimal) approximation is identified. Furthermore, the operator mapping f to its extremal best approximation is shown to be Lipschitzian with some constant C or optimal Lipschitzian having the smallest ...

In the well-studied Unsplittable Flow on a Path problem (UFP), we are given a path graph with edge capacities. Furthermore, we are given a collection of n tasks, each one characterized by a subpath, a weight, and a demand. Our goal is to select a maximum weight subset of tasks so that the total demand of selected tasks using each edge is upper bounded by the corresponding capacity. Chakaravarth...

Acoustic field calculations in underwater environments are often uncertain because the environmental parameters required for such calculations are uncertain. This letter compares the accuracy of direct simulations, the field shifting approximation, and polynomial chaos expansions for predicting acoustic amplitude uncertainty in 100-m-deep Pekeris waveguides having spatially uniform uncertain wa...

We present a polynomial time approximation scheme for Euclidean TSP in <2. Given any n nodes in the plane and > 0, the scheme finds a (1 + )-approximation to the optimum traveling salesman tour in time nO(1= ). When the nodes are in <d, the running time increases to nÕ(logd 2 n)= d 1 . The previous best approximation algorithm for the problem (due to Christofides) achieves a 3=2approximation in...

Given a graph G = (V,E) with node weight w : V → R and a subset S ⊆ V , find a minimum total weight tree interconnecting all nodes in S. This is the node-weighted Steiner tree problem which will be studied in this paper. In general, this problem is NP-hard and cannot be approximated by a polynomial time algorithm with performance ratio a lnn for any 0 < a < 1 unless NP ⊆ DTIME(n), where n is th...

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...

There are two kinds of estimates of the degree of approximation of continuous functions on [−1, 1] by algebraic polynomials, Nikolskii-type pointwise estimates and Jackson-type uniform estimates, involving either ordinary moduli of smoothness, or the DitzianTotik (DT) ones, or the recent estimates involving the weighted DTmoduli of smoothness. The purpose of this paper is to complete the table ...

Abstract We present an asymptotic analysis of adaptive methods for L p approximation functions f ∈ C r ([ a , b ]), where $1\le p\le +\infty $ 1 ≤ p + ∞ . The rely on piecewise polynomial interpolation degree − 1 with strategy selecting m sub...