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IWPEC
2009
Springer

The Parameterized Complexity of Some Geometric Problems in Unbounded Dimension

9 years 5 months ago
The Parameterized Complexity of Some Geometric Problems in Unbounded Dimension
We study the parameterized complexity of the following fundamental geometric problems with respect to the dimension d: i) Given n points in Rd, compute their minimum enclosing cylinder. ii) Given two n-point sets in Rd, 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 nΩ(d)-time lower bound (under the Exponential Time Hypothesis).
Panos Giannopoulos, Christian Knauer, Günter
Added 27 May 2010
Updated 27 May 2010
Type Conference
Year 2009
Where IWPEC
Authors Panos Giannopoulos, Christian Knauer, Günter Rote
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