A refined analysis of submodular Greedy

Many algorithms for maximizing a monotone submodular function subject to a knapsack constraint rely on the natural greedy heuristic. We present a novel refined analysis of this greedy heuristic which enables us to: (1) reduce the enumeration in the tight (1−e−1)-approximation of [Sviridenko 04] from...

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Bibliographic Details
Published in:Operations research letters Vol. 49; no. 4; pp. 507 - 514
Main Authors: Kulik, Ariel, Schwartz, Roy, Shachnai, Hadas
Format: Journal Article
Language:English
Published: Elsevier B.V 01.07.2021
Subjects:
Approximation algorithms
Knapsack constraint
Submodular functions
Submodular functions
Approximation algorithms
Knapsack constraint
ISSN:0167-6377, 1872-7468
Online Access:Get full text
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Summary:Many algorithms for maximizing a monotone submodular function subject to a knapsack constraint rely on the natural greedy heuristic. We present a novel refined analysis of this greedy heuristic which enables us to: (1) reduce the enumeration in the tight (1−e−1)-approximation of [Sviridenko 04] from subsets of size three to two; (2) present an improved upper bound of 0.42945 for the classic algorithm which returns the better between a single element and the output of the greedy heuristic.
ISSN:0167-6377
1872-7468
DOI:10.1016/j.orl.2021.04.006