Related papers: On some characterizations of greedy-type bases
The Kaczmarz method is an iterative algorithm for solving systems of linear equalities and inequalities, that iteratively projects onto these constraints. Recently, Strohmer and Vershynin [J. Fourier Anal. Appl., 15(2):262-278, 2009] gave a…
The famous $k$-means++ algorithm of Arthur and Vassilvitskii [SODA 2007] is the most popular way of solving the $k$-means problem in practice. The algorithm is very simple: it samples the first center uniformly at random and each of the…
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 present a general approximation framework for weighted integer covering problems. In a weighted integer covering problem, the goal is to determine a non-negative integer solution $x$ to system $\{ Ax \geq r \}$ minimizing a non-negative…
A lot of recent activity in the theory of cluster algebras has been directed towards various constructions of "natural" bases in them. One of the approaches to this problem was developed several years ago by P.Sherman - A.Zelevinsky who…
I provide a novel approach to characterizing the set of interim realizable allocations, in the spirit of Matthews (1984) and Border (1991). The approach allows me to identify precisely why exact characterizations are difficult to obtain in…
We show for several computational problems how classical greedy algorithms for special cases can be derived in a simple way from dynamic programs for the general case: interval scheduling (restricted to unit weights), knapsack (restricted…
The initial-value problem associated with multi-valued operators in Banach spaces is here reformulated as a minimization principle, extending results of Brezis-Ekeland, Nayroles and Fitzpatrick. At the focus there is the stability of these…
Randomized greedy algorithms form one of the simplest yet most effective approaches for computing approximate matchings in graphs. In this paper, we focus on the class of vertex-iterative (VI) randomized greedy matching algorithms, which…
In this paper we deal with four generalized notions of amenability which are called approximate, approximate weak, approximate cyclic and approximate $n$-weak amenability. The first two were introduced and studied by Ghahramani and Loy in…
It was recently shown that a version of the greedy algorithm gives a construction of fault-tolerant spanners that is size-optimal, at least for vertex faults. However, the algorithm to construct this spanner is not polynomial-time, and the…
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,…
Orthogonal greedy learning (OGL) is a stepwise learning scheme that adds a new atom from a dictionary via the steepest gradient descent and build the estimator via orthogonal projecting the target function to the space spanned by the…
In this paper, we propose a unified framework and an algorithm for the problem of group recommendation where a fixed number of items or alternatives can be recommended to a group of users. The problem of group recommendation arises…
The fields of signal and image processing have been deeply influenced by the introduction of deep neural networks. These are successfully deployed in a wide range of real-world applications, obtaining state of the art results and surpassing…
The algorithmic small-world phenomenon, empirically established by Milgram's letter forwarding experiments from the 60s, was theoretically explained by Kleinberg in 2000. However, from today's perspective his model has several severe…
Setcover greedy algorithm is a natural approximation algorithm for test set problem. This paper gives a precise and tighter analysis of performance guarantee of this algorithm. The author improves the performance guarantee $2\ln n$ which…
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…
We prove the equality of two canonical bases of a rank 2 cluster algebra, the greedy basis of Lee-Li-Zelevinsky and the theta basis of Gross-Hacking-Keel-Kontsevich.
In this article, we present a greedy algorithm based on a tensor product decomposition, whose aim is to compute the global minimum of a strongly convex energy functional. We prove the convergence of our method provided that the gradient of…