On the Complexity of Some Geometric Problems in Unbounded Dimension

This paper examines the complexity of several geometric problems due to un bounded dimension The problems considered are i minimum cover of points by unit cubes ii minimum cover of points by unit balls and iii minimum number of lines to hit a set of balls Each of these problems is proven not to have a poly nomial approximation scheme unless P NP Speci c lower bounds on the error ratios attainable in polynomial time are given assuming P NP In particular it is shown that covering by two cubes is in P while covering by three cubes is NP complete