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Labeled Pyramids with Combinatorial Maps

Luc Brun &
Walter Kropatsch.
Combinatorial Pyramids are defined as a stack of
successively reduced combinatorial maps. The Pyramid
construction plan defined in TR-63~itebrun-00-1
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 build from the
base by a one pass algorithm scanning all the darts of
the initial combinatorial map~itebrun-00-1. 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.