1 research outputs found
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 : i) Given points in \Rd,
compute their minimum enclosing cylinder. ii) Given two -point sets in
\Rd, decide whether they can be separated by two hyperplanes. iii) Given a
system of linear inequalities with 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 . %and hence not solvable
in time, for any computable function and constant
%(unless FPT=W[1]). Our reductions also give a -time lower bound
(under the Exponential Time Hypothesis)