Near-Linear Algorithms for Geometric Hitting Sets and Set Covers
Given a finite range space Σ = ( X , R ) , with N = | X | + | R | , we present two simple algorithms, based on the multiplicative-weight method, for computing a small-size hitting set or set cover of Σ . The first algorithm is a simpler variant of the Brönnimann–Goodrich algorithm but more efficient...
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| Veröffentlicht in: | Discrete & computational geometry Jg. 63; H. 2; S. 460 - 482 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
Springer US
01.03.2020
Springer Nature B.V |
| Schlagworte: | |
| ISSN: | 0179-5376, 1432-0444 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Given a finite range space
Σ
=
(
X
,
R
)
, with
N
=
|
X
|
+
|
R
|
, we present two simple algorithms, based on the multiplicative-weight method, for computing a small-size hitting set or set cover of
Σ
. The first algorithm is a simpler variant of the Brönnimann–Goodrich algorithm but more efficient to implement, and the second algorithm can be viewed as solving a two-player zero-sum game. These algorithms, in conjunction with some standard geometric data structures, lead to near-linear algorithms for computing a small-size hitting set or set cover for a number of geometric range spaces. For example, they lead to
O
(
N
polylog
(
N
)
)
expected-time randomized
O
(1)-approximation algorithms for both hitting set and set cover if
X
is a set of points and
R
a set of disks in
R
2
. |
|---|---|
| Bibliographie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0179-5376 1432-0444 |
| DOI: | 10.1007/s00454-019-00099-6 |