Canonical Decomposition of Outerplanar Maps and Application to Enumeration, Coding, and Generation (Extended Abstract)
Nicolas Bonichon, Cyril Gavoille, Nicolas Hanusse · 2003
In this article we define a canonical decomposition of rooted outerplanar maps into a spanning tree and a list of edges. This decom- position, constructible in linear time, implies the existence of bijection between rooted outerplanar maps with n nodes and bicolored rooted ordered trees with n nodes where all the nodes of the last branch are col- ored white. As a consequence, for rooted outerplanar maps of n nodes, we derive: - an enumeration formula, and an asymptotic of 2 3n−Θ(log n) ; - an optimal data structure of asymptotically 3n bits, built in O(n) time, supporting adjacency and degree queries in worst-case constant time; - an O(n) expected time uniform random generating algorithm.