Implementation and parallelization of a reverse-search algorithm for Minkowski sums

2010 Proceedings of the 12th Workshop on Algorithm Engineering and Experiments, ALENEX 2010

Volumn , Issue , 2010, Pages 34-42

  Weibel, Christophe ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

TOPOLOGY;

EXACT ARITHMETIC; HIGHER DIMENSIONS; LINEAR ACCELERATIONS; PARALLEL IMPLEMENTATIONS; PARALLEL VERSION; PARALLELIZATIONS; PERFORMANCE TESTS; REVERSE SEARCH;

LEARNING ALGORITHMS;

EID: 84879368270     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1137/1.9781611972900.4     Document Type: Conference Paper

References (16)

1. D. Avis and K. Fukuda. Reverse search for enumeration. Discrete Applied Mathematics. The Journal of Combinatorial Algorithms, Informatics and Computa- tional Sciences, 65(1-3):21-46, 1996. First International Colloquium on Graphs and Optimization (GOI), 1992 (Grimentz).
2. A. Br̈ungger, A. Marzetta, K. Fukuda, and J. Nievergelt. The parallel search bench ZRAM and its applications. Annals of Operations Research, 90:45-63, 1999.
3. A. Deza and F. Xie. Hyperplane arrangements with large average diameter. In Polyhedral Computation, volume 48 of CRM Proceedings and Lecture Notes, 2009.
4. T. G. et al. GNU multiple precision arithmetic library. http://gmplib.org/.
5. E. Fogel. Minkowski Sum Construction and other Applications of Arrangements of Geodesic Arcs on the Sphere. PhD thesis, Tel-Aviv University, Tel-Aviv, 2009.
6. E. Fogel and D. Halperin. Exact and efficient construction of Minkowski sums of convex polyhedra with applications. In Proceedings of the eigth Workshop Algo- rithm Engineering and Experiments (Alenex'06), pages 3-15, 2006.
7. K. Fukuda. From the zonotope construction to the Minkowski addition of convex polytopes. Journal of Symbolic Computation, 38(4):1261-1272, 2004.
8. K. Fukuda. Cdd and cddplus home page. Mathematics institute, ETH Zurich, 2007. http://www.ifor.math.ethz.ch/~fukuda/cdd-home.
9. M. Granados, P. Hachenberger, S. Hert, L. Kettner, K. Mehlhorn, and M. Seel. Boolean operations on 3d selective nef complexes- data structure, algorithms, and implementation. In Proceedings of the eleventhAnnual European Symposium on Algorithms, Vol 2832 of LNCS, pages 654-666. Springer, 2003.
10. P. Gritzmann and B. Sturmfels. Minkowski addition of polytopes: computational complexity and applications to Gr̈obner bases. SIAM Journal on Discrete Mathe- matics, 6(2):246-269, 1993.
11. T. Lozano-Ṕerez and M. A. Wesley. An algorithm for planning collision-free paths among polyhedral obstacles. Communications of the ACM, 22(10):560-570, 1979.
12. L. Pachter and B. Sturmfels, editors. Algebraic statis- tics for computational biology. Cambridge University Press, New York, 2005.
13. J.-P. Petit. Sṕecification ǵeoḿetrique des produits : Ḿethode de d́etermination des toĺerances. Application en conception assist́ee par ordinateur. PhD thesis, Universit́e de Savoie, 2004.
14. J. Rambau. TOPCOM: Triangulations of point configurations and oriented matroids. In A. M. Cohen, X.-S. Gao, and N. Takayama, editors, Mathematical Software-ICMS 2002, pages 330-340. World Scientific, 2002.
15. H. R. Tiwary. On the hardness of minkowski addition and related operations. In SCG '07: Proceedings of the twenty-third annual symposium on Computational geometry, pages 306-309, New York, NY, USA, 2007. ACM.
16. H. Zhang. Partially Observable Markov Decision Processes: A Geometric Technique and Analysis. Opera- tions Research, doi:10.1287/opre.1090.0697, 2009.