Linear programming and convex hulls made easy

Authors:
Raimund Seidel
Affiliations:
Computer Science Division, University of California Berkeley, Berkeley CA
Venue:
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Year:
1990

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Abstract

We present two randomized algorithms. One solves linear programs involving m constraints in d variables in expected time &Ogr;(m). The other constructs convex hulls of n points in Rd, d 3, in expected time &Ogr;(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.