A Refined Analysis of Submodular Greedy

02/25/2021

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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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A Refined Analysis of Submodular Greedy

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Revisiting Modified Greedy Algorithm for Monotone Submodular Maximization with a Knapsack Constraint

Analysis of a Greedy Heuristic for the Labeling of a Map with a Time-Window Interface

On the Unreasonable Effectiveness of the Greedy Algorithm: Greedy Adapts to Sharpness

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A Refined Analysis of Submodular Greedy

Related Research

Approximation algorithms for k-submodular maximization subject to a knapsack constraint

Submodular Maximization Under A Matroid Constraint: Asking more from an old friend, the Greedy Algorithm

Revisiting Modified Greedy Algorithm for Monotone Submodular Maximization with a Knapsack Constraint

Analysis of a Greedy Heuristic for the Labeling of a Map with a Time-Window Interface

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