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Erschienen in:
2009 | OriginalPaper | Buchkapitel
The Parameterized Complexity of Some Geometric Problems in Unbounded Dimension
verfasst von : Panos Giannopoulos, Christian Knauer, Günter Rote
Erschienen in: Parameterized and Exact Computation
Verlag: Springer Berlin Heidelberg
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We study the parameterized complexity of the following fundamental geometric problems with respect to the dimension
d
:
i) Given
n
points in ℝ
d
, compute their minimum enclosing cylinder.
ii) Given two
n
-point sets in ℝ
d
, decide whether they can be separated by two hyperplanes.
iii) Given a system of
n
linear inequalities with
d
variables, find a maximum size feasible subsystem.
We show that (the decision versions of) all these problems are W[1]-hard when parameterized by the dimension
d
. Our reductions also give a
n
Ω(
d
)
-time lower bound (under the Exponential Time Hypothesis).