A refined analysis of submodular Greedy

Ariel Kulik; Roy Schwartz; Hadas Shachnai

doi:10.1016/j.orl.2021.04.006

A refined analysis of submodular Greedy

Ariel Kulik
, Roy Schwartz
, Hadas Shachnai

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	507-514
Number of pages	8
Journal	Operations Research Letters
Volume	49
Issue number	4
DOIs	https://doi.org/10.1016/j.orl.2021.04.006
State	Published - 1 Jul 2021
Externally published	Yes

Keywords

Approximation algorithms
Knapsack constraint
Submodular functions

ASJC Scopus subject areas

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/j.orl.2021.04.006

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abstract = "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.",

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AU - Schwartz, Roy

AU - Shachnai, Hadas

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N2 - 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.

AB - 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.

KW - Approximation algorithms

KW - Knapsack constraint

KW - Submodular functions

UR - https://www.scopus.com/pages/publications/85107091463

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DO - 10.1016/j.orl.2021.04.006

M3 - Article

AN - SCOPUS:85107091463

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VL - 49

SP - 507

EP - 514

JO - Operations Research Letters

JF - Operations Research Letters

IS - 4

ER -

A refined analysis of submodular Greedy

Abstract

Keywords

ASJC Scopus subject areas

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