Greedy algorithms: a review and open problems

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 con...

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Published inJournal of inequalities and applications Vol. 2025; no. 1; pp. 11 - 22
Main Author García, Andrea
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 03.02.2025
Springer Nature B.V
SpringerOpen
Subjects
Algorithms
Analysis
Applications of Mathematics
Approximation
Banach spaces
Chebyshev approximation
Computer science
Data compression
Dictionaries
Greedy algorithm
Greedy algorithms
Greedy bases
Hilbert space
Mathematics
Mathematics and Statistics
Optimization
Review
Greedy algorithm
Greedy bases
41A46
46B15
41A65
Online AccessGet full text
ISSN1029-242X
1025-5834
1029-242X
DOI10.1186/s13660-025-03254-1

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Abstract 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 . In both cases, we conclude by posing several questions for future research.
AbstractList Abstract 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.
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 $0< p\leq 1$ 0 < p ≤ 1 . In both cases, we conclude by posing several questions for future research.
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. In both cases, we conclude by posing several questions for future research.
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 . In both cases, we conclude by posing several questions for future research.
ArticleNumber 11
Author García, Andrea
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Greedy bases
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Snippet Greedy algorithms are a fundamental class of mathematics and computer science algorithms, defined by their iterative approach of making locally optimal...
Abstract Greedy algorithms are a fundamental class of mathematics and computer science algorithms, defined by their iterative approach of making locally...
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SubjectTerms Algorithms
Analysis
Applications of Mathematics
Approximation
Banach spaces
Chebyshev approximation
Computer science
Data compression
Dictionaries
Greedy algorithm
Greedy algorithms
Greedy bases
Hilbert space
Mathematics
Mathematics and Statistics
Optimization
Review
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Title Greedy algorithms: a review and open problems
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