The acyclic directed Steiner tree problem (ADSP) requires a minimal outward tree within an acyclic digraph with edge costs G = (V; E; d) which connects a root r with a distinguished subset S V , #S = k. The best possible performance guarantee of any polynomial approximation algorithm for ADSP cannot be less than 1 4 log k unless ~ P NP. The presented series of heuristics A n has a performance g...

For each q ∈ N0, we construct positive linear polynomial approximation operators Mn that simultaneously preserve k-monotonicity for all 0 ≤ k ≤ q and yield the estimate |f(x)−Mn(f, x)| ≤ cω λ 2 ( f, nφ(x) (φ(x) + 1/n) ) , for x ∈ [0, 1] and λ ∈ [0, 2), where φ(x) := √ x(1− x) and ω 2 is the second Ditzian-Totik modulus of smoothness corresponding to the “step-weight function” ψ. In particular, ...

We study the following algorithmic problem: given n points within a finite d-dimensional box, what is the smallest number of extra points that need to be added, to ensure that every d-dimensional unit box is either empty, or contains at least k points. We motivate the problem through a possible application to data privacy. We show that minimizing the number of extra points to be added is strong...

In this paper, we present an efficient polynomial time approximation scheme (EPTAS) for scheduling on uniform processors, i.e. finding a minimum length schedule for a set of n independent jobs on m processors with different speeds (a fundamental NP-hard scheduling problem). The previous best polynomial time approximation scheme (PTAS) by Hochbaum and Shmoys has a running time of (n/ ) 2). Our a...

We consider static-priority tasks with constraineddeadlines that are subjected to release jitter. We define an approximate worst-case response-time analysis and propose a polynomial-time algorithm. For that purpose, we extend the Fully Polynomial-Time Approximation Scheme (FPTAS) presented in [6] to take into account release jitter constraints; this feasibility test is then used to define a pol...

A new algorithm is proposed for polynomial or rational approximation of the planar offset curve. The best rational Chebyshev approximation could be regarded as a kind of geometric approximation along the fixed direction. Based on this idea, we developed a wholly new offset approximation method by changing the fixed direction to the normal directions. The error vectors follow the direction of no...

We consider the approximation of measures by trigonometric polynomials with respect to p-Wasserstein distance for general p ≥ 1. While best error decreases inversely polynomial degree n every p, convolution Fejér kernel achieves just a

One of the interesting, important and attractive problems in applied mathematics is how to best approximate a function in a given space. In this paper, the problem of best approximation is considered for fuzzy functions, by optimization to obtain a fuzzy polynomial.

When implementing regular enough functions (e.g., elementary or special functions) on a computing system, we frequently use polynomial approximations. In most cases, the polynomial that best approximates (for a given distance and in a given interval) a function has coefficients that are not exactly representable with a finite number of bits. And yet, the polynomial approximations that are actua...

A general setting for constrained Z,1-approximation is presented. Let Un be a finite dimensional subspace of C[a, b] and L be a linear operator from Un to C(K) (r = 0, 1) where K is a finite union of disjoint, closed, bounded intervals. For v , u e C(K) with v < u, the approximating set is Univ, u) = {p e Un : v < Lp < u on K} and the norm is \\f\\w = Xf \f\wdx where w a positive continuous fun...