Canonical Decomposition of Outerplanar Maps and Application to Enumeration, Coding and Generation
Vol. 9, no. 2, pp. 185-204, 2005. Regular paper.
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 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 23n −Θ(logn);
  • 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.
Submitted: July 2003.
Revised: August 2005.
Communicated by Xin He
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