Labeled Pyramids with Combinatorial Maps (bibtex)

by Luc Brun, Walter Kropatsch

Abstract:

Combinatorial Pyramids are defined as a stack of successively reduced combinatorial maps. The Pyramid construction plan defined in TR-63 allows to describe a pyramid by two functions level and state defined respectively on the set of darts of the initial combinatorial map and the set of levels of the pyramid. These two functions encode respectively the maximum level on which a dart survives and the type of each reduction operation. Based on these functions any combinatorial map of the pyramid may be built from the base by a one pass algorithm scanning all the darts of the initial combinatorial map. In this technical report we show that algorithms with a same sequential and parallel complexity may be designed in order to build all the reduced combinatorial maps of the Pyramid.

Reference:

Labeled Pyramids with Combinatorial Maps (Luc Brun, Walter Kropatsch), Technical report, PRIP, TU Wien, 2003.

Bibtex Entry:

@TechReport{PTR-Brun03a, author = "Luc Brun and Walter Kropatsch", title = "Labeled {P}yramids with {C}ombinatorial {M}aps", institution = "PRIP, TU Wien", number = "PRIP-TR-082", year = "2003", url = "ftp://ftp.prip.tuwien.ac.at/pub/publications/trs/tr82.pdf", abstract = "Combinatorial Pyramids are defined as a stack of successively reduced combinatorial maps. The Pyramid construction plan defined in TR-63 allows to describe a pyramid by two functions level and state defined respectively on the set of darts of the initial combinatorial map and the set of levels of the pyramid. These two functions encode respectively the maximum level on which a dart survives and the type of each reduction operation. Based on these functions any combinatorial map of the pyramid may be built from the base by a one pass algorithm scanning all the darts of the initial combinatorial map. In this technical report we show that algorithms with a same sequential and parallel complexity may be designed in order to build all the reduced combinatorial maps of the Pyramid.", }

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