{
  "id": "2408.08935",
  "version": "v1",
  "published": "2024-08-16T09:55:44.000Z",
  "updated": "2024-08-16T09:55:44.000Z",
  "title": "Greedy algorithms: a review and open problems",
  "authors": [
    "Andrea García"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Greedy algorithms are a fundamental category of algorithms in mathematics and computer science, characterized by their iterative, locally optimal decision-making approach, which aims to find global optima. In this review, we will discuss two greedy algorithms. First, we will talk about the so-called Relaxed Greedy Algorithm in the context of dictionaries in Hilbert spaces analyzing the optimality of definition of this algorithm and, next, we give a general overview of the Thresholding Greedy Algorithm and the Chebyshev Thresholding Greedy Algorithm with regard to bases in p-Banach spaces with $0 < p \\leq 1$. In both cases, we pose some questions for future research.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-16T09:55:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "open problems",
      "chebyshev thresholding greedy algorithm",
      "hilbert spaces",
      "global optima",
      "relaxed greedy algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}