author = "Luc {B}run and Walter Kropatsch", institution ="PRIP, TU Wien", number = "PRIP-TR-yy", title = "Labeled Pyramids with Combinatorial Maps", year = 2002, theme = {hierarchical}, price = "20,-", url = {article:=ftp://www.prip.tuwien.ac.at/pub/publications/trs/tr57.ps.gz}, abstract = " Combinatorial Pyramids are defined as a stack of successively reduced combinatorial maps. The Pyramid construction plan defined in TR-63~cite{brun-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~cite{brun-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."