Canonical Decomposition of Outerplanar Maps and Application to Enumeration, Coding and Generation

Nicolas Bonichon, Cyril Gavoille, Nicolas Hanusse
2005 Journal of Graph Algorithms and Applications  
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 in the Word-RAM model, 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 2
more » ... 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 and neighbors query of a degree-d node in worst-case O(d) time. • an O(n) expected time uniform random generating algorithm.
doi:10.7155/jgaa.00105 fatcat:3xapxqyqs5h5bkpwbziwziizaa