Abstract
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.
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Farzan, A., Munro, J.I. (2008). A Uniform Approach Towards Succinct Representation of Trees. In: Gudmundsson, J. (eds) Algorithm Theory – SWAT 2008. SWAT 2008. Lecture Notes in Computer Science, vol 5124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69903-3_17
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DOI: https://doi.org/10.1007/978-3-540-69903-3_17
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