Typical model reduction methods for parametric partial differential equations construct a linear space V n which approximates well the solution manifold M consisting of all solutions u ( y ) with vector parameters. In many problems numerical computation, nonlinear such as adaptive approximation, -term and certain tree-based may provide improved efficiency over methods. Nonlinear replace by Σ . ...

Shop scheduling problems are known to be notoriously intractable, both in theory and practice. In this paper we give a randomized approximation algorithm for flow shop scheduling where the number of machines is part of the input problem. Our algorithm has a multiplicative factor of 2(1 + δ) and an additive term of O(m ln(m+ n)pmax)/δ ).

Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...

We study the streaming complexity and communication complexity of approximating unweighted semimatchings. A semi-matching in a bipartite graph G = (A,B,E) with n = |A| is a subset of edges S ⊆ E that matches all A vertices to B vertices with the goal usually being to do this as fairly as possible. While the term semi-matching was coined in 2003 by Harvey et al. [WADS 2003, also Journal of Algor...

We study nonlinear n-term approximation in Lp(R) (0 < p ≤ ∞) from hierarchical sequences of stable local bases consisting of differentiable (i.e., Cr with r ≥ 1) piecewise polynomials (splines). We construct such sequences of bases over multilevel nested triangulations of R2, which allow arbitrarily sharp angles. To quantize nonlinear nterm spline approximation, we introduce and explore a colle...

Tree approximation is a form of nonlinear wavelet approximation that appears naturally in applications such as image compression and entropy encoding. The distinction between tree approximation and the more familiar n-term wavelet approximation is that the wavelets appearing in the approximant are required to align themselves in a certain connected tree sturcture. This makes their positions eas...