The complexity of geometric problems in high dimension
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Error propagation in sparse linear systems with peptide-protein incidence matrices
ISBRA'12 Proceedings of the 8th international conference on Bioinformatics Research and Applications
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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 驴 d , compute their minimum enclosing cylinder.ii) Given two n-point sets in 驴 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 驴(d)-time lower bound (under the Exponential Time Hypothesis).