We study the unsplittable flow on a path problem (UFP) where we are given a path with non-negative edge capacities and tasks, which are characterized by a subpath, a demand, and a profit. The goal is to find the most profitable subset of tasks whose total demand does not violate the edge capacities. This problem naturally arises in many settings such as bandwidth allocation, resource constraine...

A set of phylogenetic trees with overlapping leaf sets is consistent if it can be merged without conflicts into a supertree. In this paper, we study the polynomial-time approximability of two related optimization problems called the maximum rooted triplets consistency problem (MaxRTC) and the minimum rooted triplets inconsistency problem (MinRTI) in which the input is a set R of rooted triplets...

In this paper we propose a suitable combination of two collocation methods based on the zeros Jacobi polynomials in order to approximate solution Fredholm integral equations [â??1,1]. One main interesting aspects procedure is that our approach cheaper than usual method standard Lagrange interpolation using zeros. Moreover, can successfully manage functions with algebraic singularities at endpoi...

For the uniform approximation of xα on [0, 1] by rational functions the following strong error estimate is proved: Let Enn(x, [0, 1]) denote the minimal approximation error in the uniform norm on [0, 1] of rational approximants to xα with numerator and denominator degree at most n, then the the limit lim n→∞ e √ Enn(x , [0, 1]) = 4| sinπα| holds for all α > 0.

The contourlet transform can deal effectively with images which have directional information such as contour and texture. In contrast to wavelets for which there exists many good filters, the contourlet filter design for image processing applications is still an ongoing work. Therefore, this paper presents an approach for designing the contourlet filter based on the Chebyshev best uniform appro...

Let E be a compact set in C with connected complement and positive logarithmic capacity. For any f continuous on E and analytic in the interior of E, we consider the distribution of extreme points of the error of best uniform polynomial approximation on E. Let Λ = (nj) be a subsequence of N such that nj+1/nj → 1. If, for n ∈ Λ, An(f) ⊆ ∂E denotes the set of extreme points of the error function,...

We investigate the sparse spikes deconvolution problem onto spaces of algebraic polynomials. Our framework encompasses the measure reconstruction problem from a combination of noiseless and noisy moment measurements. We study a TV-norm regularization procedure to localize the support and estimate the weights of a target discrete measure in this frame. Furthermore, we derive quantitative bounds ...