Small-dimensional linear programming and convex hulls made easy
- First Online:
- 304 Downloads
We present two randomized algorithms. One solves linear programs involvingm constraints ind variables in expected timeO(m). The other constructs convex hulls ofn points in ℝd,d>3, in expected timeO(n[d/2]). In both boundsd is considered to be a constant. In the linear programming algorithm the dependence of the time bound ond is of the formd!. The main virtue of our results lies in the utter simplicity of the algorithms as well as their analyses.
Unable to display preview. Download preview PDF.
- [AS] C. R. Aragon and R. G. Seidel, Randomized Search Trees,Proc. 30th IEEE Symp. on Foundations of Computer Science (1989), pp. 540–545.Google Scholar
- [C2] K. L. Clarkson, Las Vegas Algorithms for Linear and Integer Programming when the Dimension is Small, Manuscript(Oct. 1989): a preliminary version appeared inProc. 29th IEEE Symp. on Foundations of Computer Science (1988), pp. 452–456.Google Scholar
- [K] M. Kallay, Convex Hull Algorithms in Higher Dimensions, Manuscript (1981).Google Scholar
- [S1] R. Seidel, A Convex Hull Algorithm Optimal for Point Sets in Even Dimensions, Technical Report 81-14, Department of Computer Science, University of British Columbia (1981).Google Scholar
- [S2] R. Seidel, Constructing Higher-Dimensional Convex Hulls at Logarithmic Cost per Face,Proc. 18th ACM Symp. on Theory of Computing (1986), pp. 404–413.Google Scholar
- [S3] R. Seidel, Backwards Analysis of Randomized Geometric Algorithms (Manuscript).Google Scholar