Related papers: On the Convergence of a Weak Greedy Algorithm for …

We connect high-dimensional subset selection and submodular maximization. Our results extend the work of Das and Kempe (2011) from the setting of linear regression to arbitrary objective functions. For greedy feature selection, this…

We present convergence estimates of two types of greedy algorithms in terms of the metric entropy of underlying compact sets. In the first part, we measure the error of a standard greedy reduced basis method for parametric PDEs by the…

Maximum weight matching is one of the most fundamental combinatorial optimization problems with a wide range of applications in data mining and bioinformatics. Developing distributed weighted matching algorithms is challenging due to the…

Decision Tree is a classic formulation of active learning: given $n$ hypotheses with nonnegative weights summing to 1 and a set of tests that each partition the hypotheses, output a decision tree using the provided tests that uniquely…

We address the problems of minimizing and of maximizing the spectral radius overa compact family of non-negative matrices. Those problems being hard in generalcan be efficiently solved for some special families. We consider the so-called…

We describe an adaptive greedy algorithm for Thiele continued-fraction approximation of a function defined on a continuum domain in the complex plane. The algorithm iteratively selects interpolation nodes from an adaptively refined set of…

We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation…

We extend the notion of chip-firing to weighted graphs, and generalize the Greedy Algorithm and Dhar's Burning Algorithm to weighted graphs. For a vertex $q \in V(\Gamma)$, we give an upper bound for the number of linearly equivalent…

It is a survey on recent results in constructive sparse approximation. Three directions are discussed here: (1) Lebesgue-type inequalities for greedy algorithms with respect to a special class of dictionaries, (2) constructive sparse…

We implement and test the performances of several approximation algorithms for computing the minimum dominating set of a graph. These algorithms are the standard greedy algorithm, the recent LP rounding algorithms and a hybrid algorithm…

Consider two ordered positive real number arrays of equal size. The problem is to find such set of indices of given size that the ratio of the sums of the array elements with those indices is minimized. In this work, in order to mitigate…

Let $T$ be a Fourier integral operator of order $-(n-1)/2$ associated with a canonical relation locally parametrised by a real-phase function. A fundamental result due to Seeger, Sogge, and Stein proved in the 90's, gives the boundedness of…

The definition of $1$-planar graphs naturally extends graph planarity, namely a graph is $1$-planar if it can be drawn in the plane with at most one crossing per edge. Unfortunately, while testing graph planarity is solvable in linear time,…

A deterministic approximation algorithm is presented for the maximization of non-monotone submodular functions over a ground set of size $n$ subject to cardinality constraint $k$; the algorithm is based upon the idea of interlacing two…

Let $H$ be a Hilbert space. We investigate the properties of weak limit points of iterates of random projections onto $K\geq 2$ closed convex sets in $H$ and the parallel properties of weak limit points of residuals of random greedy…

In this paper we develop a procedure to deal with a family of parameter-dependent ill-posed problems, for which the exact solution in general does not exist. The original problems are relaxed by considering corresponding approximate ones,…

In order to prove weak convergence of the periodic multiplicative Selmer algorithm we ensure that the periodicity matrix is positive and establish a relation between its entries and eigenvalues. Since we can imply that the limit of these…

Recently, it has been discovered that results on universal sampling discretization of the square norm are useful in sparse sampling recovery with error being measured in the square norm. It was established that a simple greedy type…

In this paper, we study greedy variants of quasi-Newton methods. They are based on the updating formulas from a certain subclass of the Broyden family. In particular, this subclass includes the well-known DFP, BFGS and SR1 updates. However,…

We consider an optimization problem where the decision variable is a string of bounded length. For some time there has been an interest in bounding the performance of the greedy strategy for this problem. Here, we provide weakened…