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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