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...

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...

Abstract. Let φm be a polynomial satisfying some mild conditions. Given a set R ⊂ C, a continuous function f on R and its best approximation p n−1 from Πn−1 with respect to the maximum norm, we show that p ∗ n−1 ◦φm is a best approximation to f ◦ φm on the inverse polynomial image S of R, i.e. φm(S) = R, where the extremal signature is given explicitly. A similar result is presented for constra...

the main purpose of this paper is to find t-best approximations in fuzzy normed spaces. we introduce the notions of t-proximinal sets and f-approximations and prove some interesting theorems. in particular, we investigate the set of all t-best approximations to an element from a set.

The main purpose of this paper is to consider the t-best simultaneousapproximation in fuzzy normed spaces. We develop the theory of t-bestsimultaneous approximation in quotient spaces. Then, we discuss the relationshipin t-proximinality and t-Chebyshevity of a given space and its quotientspace.

The main purpose of this paper is to find t-best approximations in fuzzy normed spaces. We introduce the notions of t-proximinal sets and F-approximations and prove some interesting theorems. In particular, we investigate the set of all t-best approximations to an element from a set.

Connected Vertex Cover Problem (CVC) is an NP -hard problem. The currently best known approximation algorithm for CVC has performance ration 2. This paper gives the first Polynomial Time Approximation Scheme for CVC in Unit Disk Graph.