Computational Complexity of Combinatorial Surfaces

Gert Vegter, Chee K. Yap

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

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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 languageEnglish
Title of host publicationEPRINTS-BOOK-TITLE
PublisherUniversity of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science
Number of pages10
Publication statusPublished - 1990

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