Robust monotone submodular function maximization
We consider a robust formulation, introduced by Krause et al. (J Artif Intell Res 42:427–486, 2011 ), of the classical cardinality constrained monotone submodular function maximization problem, and give the first constant factor approximation results. The robustness considered is w.r.t. adversarial...
Uložené v:
| Vydané v: | Mathematical programming Ročník 172; číslo 1-2; s. 505 - 537 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.11.2018
Springer Nature B.V |
| Predmet: | |
| ISSN: | 0025-5610, 1436-4646 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Shrnutí: | We consider a robust formulation, introduced by Krause et al. (J Artif Intell Res 42:427–486,
2011
), of the classical cardinality constrained monotone submodular function maximization problem, and give the first constant factor approximation results. The robustness considered is w.r.t. adversarial removal of up to
τ
elements from the chosen set. For the fundamental case of
τ
=
1
, we give a deterministic
(
1
-
1
/
e
)
-
1
/
Θ
(
m
)
approximation algorithm, where
m
is an input parameter and number of queries scale as
O
(
n
m
+
1
)
. In the process, we develop a deterministic
(
1
-
1
/
e
)
-
1
/
Θ
(
m
)
approximate greedy algorithm for bi-objective maximization of (two) monotone submodular functions. Generalizing the ideas and using a result from Chekuri et al. (in: FOCS 10, IEEE, pp 575–584,
2010
), we show a randomized
(
1
-
1
/
e
)
-
ϵ
approximation for constant
τ
and
ϵ
≤
1
Ω
~
(
τ
)
, making
O
(
n
1
/
ϵ
3
)
queries. Further, for
τ
≪
k
, we give a fast and practical 0.387 algorithm. Finally, we also give a black box result result for the much more general setting of robust maximization subject to an Independence System. |
|---|---|
| Bibliografia: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0025-5610 1436-4646 |
| DOI: | 10.1007/s10107-018-1320-2 |