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<p>Greedy algorithms are a fundamental class of mathematics and computer science algorithms, defined by their iterative approach of making locally optimal decisions to approximate global optima. In this review, we focus on two greedy algorithms. First, we examine the relaxed greedy algorithm in the context of dictionaries in Hilbert spaces, analyzing the optimality of the definition of this algorithm. Next, we provide a general overview of the thresholding greedy algorithm and the Chebyshev thresholding greedy algorithm, with particular attention to their applications to bases in <i>p</i>-Banach spaces with <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3254_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="72" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mn>0</mn> <mo>&lt;</mo> <mi>p</mi> <mo>≤</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$0&lt; p\leq 1$</EquationSource> </InlineEquation>. In both cases, we conclude by posing several questions for future research.</p>

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Greedy algorithms: a review and open problems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月3日

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  • Andrea García

摘要

Greedy algorithms are a fundamental class of mathematics and computer science algorithms, defined by their iterative approach of making locally optimal decisions to approximate global optima. In this review, we focus on two greedy algorithms. First, we examine the relaxed greedy algorithm in the context of dictionaries in Hilbert spaces, analyzing the optimality of the definition of this algorithm. Next, we provide a general overview of the thresholding greedy algorithm and the Chebyshev thresholding greedy algorithm, with particular attention to their applications to bases in p-Banach spaces with 0 < p ≤ 1 $0< p\leq 1$ . In both cases, we conclude by posing several questions for future research.