New modification of the double description method for constructing the skeleton of a polyhedral cone
- 149 Downloads
A new modification of the double description method is proposed for constructing the skeleton of a polyhedral cone. Theoretical results and a numerical experiment show that the modification is considerably superior to the original algorithm in terms of speed.
Keywordspolyhedron polyhedral cone skeleton of a cone convex hull double description method
Unable to display preview. Download preview PDF.
- 1.F. Preparata and M. Shamos, Computational Geometry: An Introduction (Springer-Verlag, New York, 1985; Mir, Moscow, 1989).Google Scholar
- 3.T. S. Motzkin, H. Raiffa, G. L. Thompson, and R. M. Thrall, “The Double Description Method,” Contributions to the Theory of Games (Princeton University Press, Princeton, N. J., 1953; Fizmatgiz, Moscow, 1961).Google Scholar
- 7.S. N. Chernikov, Linear Inequalities (Nauka, Moscow, 1968) [in Russian].Google Scholar
- 8.S. I. Veselov, I. E. Parubochii, and V. N. Shevchenko, “A Software Program for Finding the Skeleton of the Cone of Nonnegative Solutions of a System of Linear Inequalities,” in System and Applied Software Programs (Gor’kov. Gos. Univ., Gor’kii, 1984), pp. 83–92 [in Russian].Google Scholar
- 9.F. Fernandez and P. Quinton, “Extension of Chernikova’s Algorithm for Solving General Mixed Linear Programming Problems,” Res. Rep. RR-0943 (INRIA, Rennes, 1988).Google Scholar
- 10.H. Le Verge, “A Note on Chernikova’s Algorithm,” Res. Rep. RR-1662 (INRIA, Rennes, 1992).Google Scholar
- 11.K. Fukuda and A. Prodon, “Double Description Method Revisited,” Combinatorics and Computer Science (Springer-Verlag, New York, 1996), pp. 91–111.Google Scholar
- 12.V. N. Shevchenko and A. Yu. Chirkov, “On the Complexity of Finding the Skeleton of a Cone,” Proceedings of 10th All-Russia Conference on Mathematical Programming and Applications (Ural. Otd. Ross. Akad. Nauk, Yekaterinburg, 1997), p. 237.Google Scholar
- 15.B. Chaselle, “An Optimal Convex Hull Algorithm in Any Fixed Dimension,” Discrete Comput. Geom., No. 10, 377–409 (1993).Google Scholar
- 18.N. Yu. Zolotykh and S. S. Lyalin, “A Parallel Algorithm for Finding the General Solution of the System of Linear Inequalities,” Vestn. Nizhegorod. Gos. Univ., No. 5, 193–199 (2009).Google Scholar