# Small-dimensional linear programming and convex hulls made easy

Article

- First Online:

- Received:
- Revised:

DOI: 10.1007/BF02574699

- Cite this article as:
- Seidel, R. Discrete Comput Geom (1991) 6: 423. doi:10.1007/BF02574699

- 68 Citations
- 250 Views

## Abstract

We present two randomized algorithms. One solves linear programs involving*m* constraints in*d* variables in expected time*O(m)*. The other constructs convex hulls of*n* points in ℝ^{d},*d*>3, in expected time*O(n*^{[d/2])}. In both bounds*d* is considered to be a constant. In the linear programming algorithm the dependence of the time bound on*d* is of the form*d*!. The main virtue of our results lies in the utter simplicity of the algorithms as well as their analyses.

## Copyright information

© Springer-Verlag New York Inc 1991