Greedy algorithms: a review and open problems

Abstract

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 $0&lt; p\leq 1$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>0</mml:mn> <mml:mo>&lt;</mml:mo> <mml:mi>p</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>1</mml:mn> </mml:math> . In both cases, we conclude by posing several questions for future research.

Topics & Concepts