###
Irregular Pyramids with Combinatorial Maps

L. Brun &
Walter Kropatsch.
This paper presents a new formalism for
irregular pyramids based on combinatorial
maps. Such pyramid consists of a stack of
successively reduced graph. Each smaller graph
is deduced from the preceding one by a set of
edges which have to be contracted or
removed. In order to perform parallel
contractions or removals, the set of edges to
be contracted or removed has to verify some
properties. Such a set of edges is called a
Decimation Parameter. A combinatorial map
encodes a planar graph thanks to two
permutations encoding the edges and their
orientation around the vertices. Combining the
useful properties of both combinatorial maps
and irregular pyramids offers a potential
alternative for representing structures at
multiple levels of abstraction.