### Abstract

We investigate the computational problems associated with combinatorial surfaces. Specifically, we present an algorithm (based on the Brahana-Dehn-Heegaard approach) for transforming the polygonal schema of a closed triangulated surface into its canonical form in O(n log n) time, where n is the total number of vertices, edges and faces. We also give an O(n log n + gn) algorithm for constructing canonical generators of the fundamental group of a surface of genus g. This is useful in constructing homeomorphisms between combinatorial surfaces.

Original language | English (US) |
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Title of host publication | Proc Sixth Annu Symp Comput Geom |

Publisher | Publ by ACM |

Pages | 102-111 |

Number of pages | 10 |

ISBN (Print) | 0897913620 |

State | Published - 1990 |

Event | Proceedings of the Sixth Annual Symposium on Computational Geometry - Berkeley, CA, USA Duration: Jun 6 1990 → Jun 8 1990 |

### Other

Other | Proceedings of the Sixth Annual Symposium on Computational Geometry |
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City | Berkeley, CA, USA |

Period | 6/6/90 → 6/8/90 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proc Sixth Annu Symp Comput Geom*(pp. 102-111). Publ by ACM.

**Computational complexity of combinatorial surfaces.** / Vegter, Gert; Yap, Chee.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proc Sixth Annu Symp Comput Geom.*Publ by ACM, pp. 102-111, Proceedings of the Sixth Annual Symposium on Computational Geometry, Berkeley, CA, USA, 6/6/90.

}

TY - GEN

T1 - Computational complexity of combinatorial surfaces

AU - Vegter, Gert

AU - Yap, Chee

PY - 1990

Y1 - 1990

N2 - We investigate the computational problems associated with combinatorial surfaces. Specifically, we present an algorithm (based on the Brahana-Dehn-Heegaard approach) for transforming the polygonal schema of a closed triangulated surface into its canonical form in O(n log n) time, where n is the total number of vertices, edges and faces. We also give an O(n log n + gn) algorithm for constructing canonical generators of the fundamental group of a surface of genus g. This is useful in constructing homeomorphisms between combinatorial surfaces.

AB - We investigate the computational problems associated with combinatorial surfaces. Specifically, we present an algorithm (based on the Brahana-Dehn-Heegaard approach) for transforming the polygonal schema of a closed triangulated surface into its canonical form in O(n log n) time, where n is the total number of vertices, edges and faces. We also give an O(n log n + gn) algorithm for constructing canonical generators of the fundamental group of a surface of genus g. This is useful in constructing homeomorphisms between combinatorial surfaces.

UR - http://www.scopus.com/inward/record.url?scp=0025054885&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025054885&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0025054885

SN - 0897913620

SP - 102

EP - 111

BT - Proc Sixth Annu Symp Comput Geom

PB - Publ by ACM

ER -