On maximizing monotone or non-monotone k-submodular functions with the intersection of knapsack and matroid constraints
A k -submodular function is a generalization of a submodular function. The definition domain of a k -submodular function is a collection of k -disjoint subsets instead of simple subsets of ground set. In this paper, we consider the maximization of a k -submodular function with the intersection of a...
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| Veröffentlicht in: | Journal of combinatorial optimization Jg. 45; H. 3; S. 93 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
Springer US
01.04.2023
Springer Nature B.V |
| Schlagworte: | |
| ISSN: | 1382-6905, 1573-2886 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | A
k
-submodular function is a generalization of a submodular function. The definition domain of a
k
-submodular function is a collection of
k
-disjoint subsets instead of simple subsets of ground set. In this paper, we consider the maximization of a
k
-submodular function with the intersection of a knapsack and
m
matroid constraints. When the
k
-submodular function is monotone, we use a special analytical method to get an approximation ratio
1
m
+
2
(
1
-
e
-
(
m
+
2
)
)
for a nested greedy and local search algorithm. For non-monotone case, we can obtain an approximate ratio
1
m
+
3
(
1
-
e
-
(
m
+
3
)
)
. |
|---|---|
| Bibliographie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1382-6905 1573-2886 |
| DOI: | 10.1007/s10878-023-01021-w |