Maximizing monotone submodular functions over the integer lattice
The problem of maximizing non-negative monotone submodular functions under a certain constraint has been intensively studied in the last decade. In this paper, we address the problem for functions defined over the integer lattice. Suppose that a non-negative monotone submodular function f : Z + n →...
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Veröffentlicht in: | Mathematical programming 2018-11, Vol.172 (1-2), p.539-563 |
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Sprache: | eng |
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Zusammenfassung: | The problem of maximizing non-negative monotone submodular functions under a certain constraint has been intensively studied in the last decade. In this paper, we address the problem for functions defined over the integer lattice. Suppose that a non-negative monotone submodular function
f
:
Z
+
n
→
R
+
is given via an evaluation oracle. Assume further that
f
satisfies the diminishing return property, which is not an immediate consequence of submodularity when the domain is the integer lattice. Given this, we design polynomial-time
(
1
-
1
/
e
-
ϵ
)
-approximation algorithms for a cardinality constraint, a polymatroid constraint, and a knapsack constraint. For a cardinality constraint, we also provide a
(
1
-
1
/
e
-
ϵ
)
-approximation algorithm with slightly worse time complexity that does not rely on the diminishing return property. |
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ISSN: | 0025-5610 1436-4646 |
DOI: | 10.1007/s10107-018-1324-y |