Canonical decomposition of outerplanar maps and application to enumeration, coding, and generation: (Extended Abstract)

Abstract

In this article we define a canonical decomposition of rooted outerplanar maps into a spanning tree and a list of edges. This decomposition, 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 colored white. As a consequence, for rooted outerplanar maps of n nodes, we derive: - an enumeration formula, and an asymptotic of 23n-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. © Springer-Verlag Berlin Heidelberg 2003.