Publication
Journal of Symbolic Computation
Paper

On the complexity of some geometric problems in unbounded dimension

View publication

Abstract

This paper examines the complexity of several geometric problems due to unbounded 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 polynomial approximation scheme unless P = NP. Specific 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. © 1990, Academic Press Limited. All rights reserved.

Date

Publication

Journal of Symbolic Computation

Authors

Topics

Share