Related papers: On greedy approximation in complex Banach spaces
We consider classes of objective functions of cardinality constrained maximization problems for which the greedy algorithm guarantees a constant approximation. We propose the new class of $\gamma$-$\alpha$-augmentable functions and prove…
We study the problem of fairly allocating a set of indivisible goods among agents with additive valuations. The extent of fairness of an allocation is measured by its Nash social welfare, which is the geometric mean of the valuations of the…
In the Shortest Common Superstring problem, one needs to find the shortest superstring for a set of strings. This problem is APX-hard, and many approximation algorithms were proposed, with the current best approximation factor of 2.466.…
We analyze greedy algorithms for the Hierarchical Aggregation (HAG) problem, a strategy introduced in [Jia et al., KDD 2020] for speeding up learning on Graph Neural Networks (GNNs). The idea of HAG is to identify and remove redundancies in…
Compressive sampling (CoSa) has provided many methods for signal recovery of signals compressible with respect to an orthonormal basis. However, modern applications have sparked the emergence of approaches for signals not sparse in an…
We describe the Greedy Sparse Subspace Clustering (GSSC) algorithm providing an efficient method for clustering data belonging to a few low-dimensional linear or affine subspaces from incomplete corrupted and noisy data. We provide…
We have derived that on certain Banach spaces having a graph structure $G$, the iterations for asymptotically $G$-nonexpansive map will converge weakly towards a fixed point. This result unifies and extends several theorems on fixed points…
Submodular maximization has been widely studied over the past decades, mostly because of its numerous applications in real-world problems. It is well known that the standard greedy algorithm guarantees a worst-case approximation factor of…
Kernel methods are versatile tools for function approximation and surrogate modeling. In particular, greedy techniques offer computational efficiency and reliability through inherent sparsity and provable convergence. Inspired by the…
We generalize the theory of Wiener amalgam spaces on locally compact groups to quasi-Banach spaces. As a main result we provide convolution relations for such spaces. Also we weaken the technical assumption that the global component is…
An important research thread in algorithmic game theory studies the design of efficient truthful mechanisms that approximate the optimal social welfare. A fundamental question is whether an \alpha-approximation algorithm translates into an…
This paper is devoted to the theoretical study of the efficiency, namely, stability of some greedy algorithms. In the greedy approximation theory researchers are mostly interested in the following two important properties of an algorithm --…
We prove that if $\mathcal{X}$ is a quasi-greedy Markushevich basis of a Banach space $\mathbb{X}$, its dual basis $\mathcal{X}^*$ spans a norming subspace of $\mathbb{X}^*$. We also prove this result for weaker forms of quasi-greediness,…
We develop a general, functional calculus approach to approximation of $C_0$-semigroups on Banach spaces by bounded completely monotone functions of their generators. The approach comprises most of well-known approximation formulas, yields…
The problem of column subset selection has recently attracted a large body of research, with feature selection serving as one obvious and important application. Among the techniques that have been applied to solve this problem, the greedy…
The reconstruction of unknown functions from a finite number of samples is a fundamental challenge in pure and applied mathematics. This survey provides a comprehensive overview of recent developments in sampling recovery, focusing on the…
Kernel-based methods provide flexible and accurate algorithms for the reconstruction of functions from meshless samples. A major question in the use of such methods is the influence of the samples locations on the behavior of the…
Existence and uniqueness as well as the iterative approximation of fixed points of enriched almost contractions in Banach spaces are studied. The obtained results are generalizations of the great majority of metric fixed point theorems, in…
A novel and detailed convergence analysis is presented for a greedy algorithm that was previously introduced for operator reconstruction problems in the field of quantum mechanics. This algorithm is based on an offline/online decomposition…
Online learning algorithms, widely used to power search and content optimization on the web, must balance exploration and exploitation, potentially sacrificing the experience of current users in order to gain information that will lead to…