A Uniform Approach Towards Succinct Representation of Trees

  • Arash Farzan
  • J. Ian Munro
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5124)


We propose a uniform approach for succinct representation of various families of trees. The method is based on two recursive decomposition of trees into subtrees. Recursive decomposition of a structure into substructures is a common technique in succinct data structures and has been shown fruitful in succinct representation of ordinal trees [7,10] and dynamic binary trees [16,21]. We take an approach that simplifies the existing representation of ordinal trees while allowing the full set of navigational operations. The approach applied to cardinal (i.e. k-ary) trees yields a space-optimal succinct representation allowing cardinal-type operations (e.g. determining child labeled i) as well as the full set of ordinal-type operations (e.g. reporting the number of siblings to the left of a node). Existing space-optimal succinct representations had not been able to support both types of operations [2,19].

We demonstrate how the approach can be applied to obtain a space-optimal succinct representation for the family of free trees where the order of children is insignificant. Furthermore, we show that our approach can be used to obtain entropy-based succinct representations. We show that our approach matches the degree-distribution entropy suggested by Jansson et al. [13]. We discuss that our approach can be made adaptive to various other entropy measures.


Lookup Table Free Tree Dummy Node Recursive Decomposition Succinct Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Arash Farzan
    • 1
  • J. Ian Munro
    • 1
  1. 1.School of Computer ScienceUniversity of WaterlooWaterlooCanada

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