Greedy algorithms: a review and open problems
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 i...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-02-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-025-03254-1 |
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| _version_ | 1823861475014344704 |
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| author | Andrea García |
| author_facet | Andrea García |
| author_sort | Andrea García |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-72fb9a44383b4cadaf2b2a85bc1229fe |
| institution | Kabale University |
| issn | 1029-242X |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj-art-72fb9a44383b4cadaf2b2a85bc1229fe2025-02-09T12:59:34ZengSpringerOpenJournal of Inequalities and Applications1029-242X2025-02-012025112210.1186/s13660-025-03254-1Greedy algorithms: a review and open problemsAndrea García0Universidad San Pablo-CEU, CEU UniversitiesAbstract 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.https://doi.org/10.1186/s13660-025-03254-1Greedy algorithmGreedy bases |
| spellingShingle | Andrea García Greedy algorithms: a review and open problems Journal of Inequalities and Applications Greedy algorithm Greedy bases |
| title | Greedy algorithms: a review and open problems |
| title_full | Greedy algorithms: a review and open problems |
| title_fullStr | Greedy algorithms: a review and open problems |
| title_full_unstemmed | Greedy algorithms: a review and open problems |
| title_short | Greedy algorithms: a review and open problems |
| title_sort | greedy algorithms a review and open problems |
| topic | Greedy algorithm Greedy bases |
| url | https://doi.org/10.1186/s13660-025-03254-1 |
| work_keys_str_mv | AT andreagarcia greedyalgorithmsareviewandopenproblems |