Peixin Ye Nankai University, China [email protected] In this talk we discuss which properties of a basis are important for certain direct and inverse theorems in nonlinear approximation. We study greedy approximation with regard to bases with different properties. We consider bases that are tensor products of univariate greedy bases. Some results known for unconditional bases, such as Lebesgue...

We consider load balancing of temporary tasks on m machines in the restricted assignment model. It is known that the best competitive ratio for this problem is Θ( √ m). This bound is not achieved by the greedy algorithm whose competitive ratio is known to be Ω(m 2 3 ). We give an alternative analysis to the greedy algorithm which is better than the known analysis for relatively small values of ...

We consider forward-backward greedy algorithms for solving sparse feature selection problems with general convex smooth functions. A state-of-the-art greedy method, the ForwardBackward greedy algorithm (FoBa-obj) requires to solve a large number of optimization problems, thus it is not scalable for large-size problems. The FoBa-gdt algorithm, which uses the gradient information for feature sele...

We provide new approximation guarantees for greedy low rank matrix estimation under standard assumptions of restricted strong convexity and smoothness. Our novel analysis also uncovers previously unknown connections between the low rank estimation and combinatorial optimization, so much so that our bounds are reminiscent of corresponding approximation bounds in submodular maximization. Addition...

Iterative approximation algorithms are successfully applied in parametric approximation tasks. In particular, reduced basis methods make use of the so called Greedy algorithm for approximating solution sets of parametrized partial differential equations. Recently, a-priori convergence rate statements for this algorithm have been given (Buffa et al 2009, Binev et al. 2010). The goal of the curre...

For a graph G and an order a on V(G), we define a greedy defining set as a subset S of V(G) with an assignment of colors to vertices in S, such that the pre-coloring can be extended to a x( G)-coloring of G by the greedy coloring of (G, a). A greedy defining set ofaX( G)-coloring C of G is a greedy defining set, which results in the coloring C (by the greedy procedure). We denote the size of a ...

In the general search problem we want to identify a specific element using a set of allowed tests. The general goal is to minimize the number of tests performed, although different measures are used to capture this goal. In this work we introduce a novel greedy approach that achieves the best known approximation ratios simultaneously for many different variations of this identification problem....

We consider forward-backward greedy algorithms for solving sparse feature selection problems with general convex smooth functions. A state-of-the-art greedy method, the ForwardBackward greedy algorithm (FoBa-obj) requires to solve a large number of optimization problems, thus it is not scalable for large-size problems. The FoBa-gdt algorithm, which uses the gradient information for feature sele...

Phylogenetic diversity (PD) is a measure of the extent to which different subsets of taxa span an evolutionary tree, and provides a quantitative tool for studying biodiversity conservation. Recently, it was shown that the problem of finding subsets of taxa of given size to maximize PD can be efficiently solved by a greedy algorithm. In this paper, we extend this earlier work, beginning with a m...

In this lecture we consider dynamics of a load balancing system. We study the number of steps required to reach pure Nash equilibrium in a system of ”selfish” and greedy players (jobs). We are interested in the convergence time to Nash equilibrium, rather than the quality of the allocation. We consider a variety of load balancing models including identical, restricted, related and unrelated mac...