Splitting (complicated) surfaces is hard

Computational Geometry: Theory and Applications

Volumn 41, Issue 1-2, 2008, Pages 94-110

  Chambers, Erin W ^a   Colin De Verdière, Éric ^b   Erickson, Jeff ^a   Lazarus, Francis ^c   Whittlesey, Kim ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b ECOLE NORMALE SUPÉRIEURE   (France)

^c CNRS   (France)

Author keywords

Combinatorial surfaces; Computational topology; Homotopy

Indexed keywords

EID: 84867931013     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.comgeo.2007.10.010     Document Type: Conference Paper

References (20)

1. J. Blömer, Computing sums of radicals in polynomial time, in: Proc. 32nd Annu. IEEE Sympos. Found. Comput. Sci., 1991, pp. 670-677
2. S. Cabello, Many distances in planar graphs, in: Proc. 17th Annu. ACM-SIAM Sympos. Discrete Algorithms, 2006, pp. 1213-1220
3. S. Cabello, and B. Mohar Finding shortest non-separating and non-contractible cycles for topologically embedded graphs Proc. 13th Annu. European Sympos. Algorithms Lecture Notes in Computer Science vol. 3669 2005 Springer-Verlag 131 142
4. J. Chen, and Y. Han Shortest paths on a polyhedron, part I: Computing shortest paths Int. J. Comput. Geom. Appl. 6 2 1996 127 144
5. É. Colin de Verdière, J. Erickson, Tightening non-simple paths and cycles on surfaces, in: Proc. 17th Annu. ACM-SIAM Sympos. Discrete Algorithms, 2006, pp. 192-201
6. É. Colin de Verdière, and F. Lazarus Optimal pants decompositions and shortest homotopic cycles on an orientable surface Proc. 11th Sympos. Graph Drawing Lecture Notes Comput. Sci. vol. 2912 2003 Springer-Verlag 478 490
7. É. Colin de Verdière, and F. Lazarus Optimal systems of loops on an orientable surface Discrete Comput. Geom. 33 3 2005 507 534
8. D. Eppstein Finding the k shortest paths SIAM J. Computing 28 2 1998 652 673
9. J. Erickson, and S. Har-Peled Optimally cutting a surface into a disk Discrete Comput. Geom. 31 1 2004 37 59
10. J. Erickson, K. Whittlesey, Greedy optimal homotopy and homology generators, in: Proc. 16th Annu. ACM-SIAM Sympos. Discrete Algorithms, 2005, pp. 1038-1046
11. G.N. Frederickson Fast algorithms for shortest paths in planar graphs, with applications SIAM J. Comput. 16 6 1987 1004 1022
12. A. Hatcher Algebraic Topology 2002 Cambridge University Press http://www.math.cornell.edu/~hatcher/
13. A. Itai, C.H. Papadimitriou, and J.L. Szwarcfiter Hamilton paths in grid graphs SIAM J. Comput. 11 1982 676 686
14. M. Kutz, Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear time, in: Proc. 22nd Annu. ACM Sympos. Comput. Geom., 2006, pp. 430-437
15. F. Lazarus, M. Pocchiola, G. Vegter, A. Verroust, Computing a canonical polygonal schema of an orientable triangulated surface, in: Proc. 17th Annu. ACM Sympos. Comput. Geom., 2001, pp. 80-89
16. J.S.B. Mitchell, D.M. Mount, and C.H. Papadimitriou The discrete geodesic problem SIAM J. Comput. 16 4 1987 647 668
17. B. Mohar, and C. Thomassen Graphs on Surfaces 2001 Johns Hopkins University Press
18. J. Stillwell Classical Topology and Combinatorial Group Theory 1993 Springer-Verlag New York
19. J. Takahashi, H. Suzuki, and T. Nishizeki Shortest noncrossing paths in plane graphs Algorithmica 16 1996 339 357
20. A. Zomorodian Topology for Computing 2005 Cambridge University Press