Succinct ordinal trees with level-ancestor queries

  • Authors:

  • Richard F. Geary;Rajeev Raman;Venkatesh Raman

  • Affiliations:

  • University of Leicester, Leicester, UK;University of Leicester, Leicester, UK;Institute of Mathematical Sciences, Chennai, India

  • Venue:
  • SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
  • Year:
  • 2004

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Abstract

We consider suc cinct or space-efficient representations of trees that efficiently support a variety of navigation operations. We focus on static ordinal trees, i.e., arbitrary static rooted trees where the children of each node are ordered. The set of operations is essentially the union of the sets of operations supported by previous succinct representations (Jacobson, Proc. 30th FOCS, 549--554, 1989; Munro and Raman, SIAM J. Comput. 31 (2001), 762--776; and Benoit et. al Proc. 6th WADS, LNCS 1663, 169--180, 1999), to which we add the level-ancestor operation.Our representation takes 2n + o(n) bits to represent an n-node tree, which is within o(n) bits of the information-theoretic minimum, and supports all operations in O(1) time on the RAM model. These operations also provide a mapping from the n nodes of the tree onto the integers {1,...,n}. In addition to the existing motivations for studying such data structures, we are motivated by the problem of representing XML documents compactly so that XPath queries can be supported efficiently.