Multiple knapsack-constrained monotone DR-submodular maximization on distributive lattice

We consider a problem of maximizing a monotone DR-submodular function under multiple order-consistent knapsack constraints on a distributive lattice. Because a distributive lattice is used to represent a dependency constraint, the problem can represent a dependency constrained version of a submodula...

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Vydané v:Mathematical programming Ročník 194; číslo 1-2; s. 85 - 119
Hlavní autori: Maehara, Takanori, Nakashima, So, Yamaguchi, Yutaro
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Heidelberg Springer 01.07.2022
Springer Nature B.V
Predmet:
Algorithms
Constraints
Greedy algorithms
Lattices
Maximization
Optimization
ISSN:0025-5610, 1436-4646
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Shrnutí:We consider a problem of maximizing a monotone DR-submodular function under multiple order-consistent knapsack constraints on a distributive lattice. Because a distributive lattice is used to represent a dependency constraint, the problem can represent a dependency constrained version of a submodular maximization problem on a set. We propose a ( [Formula omitted])-approximation algorithm for this problem. To achieve this result, we generalize the continuous greedy algorithm to distributive lattices: We choose a median complex as a continuous relaxation of the distributive lattice and define the multilinear extension on it. We show that the median complex admits special curves, named uniform linear motions. The multilinear extension of a DR-submodular function is concave along a positive uniform linear motion, which is a key property used in the continuous greedy algorithm.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-021-01620-7