Small-dimensional linear programming and convex hulls made easy

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 ℝd, 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. © 1991 Springer-Verlag New York Inc.