Succinct Ordinal Trees Based on Tree Covering

  • Meng He
  • J. Ian Munro
  • S. Srinivasa Rao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4596)

Abstract

Various methods have been used to represent a tree of n nodes in essentially the information-theoretic minimum space while supporting various navigational operations in constant time, but different representations usually support different operations. Our main contribution is a succinct representation of ordinal trees, based on that of Geary et al. (7), that supports all the navigational operations supported by various succinct tree representations while requiring only 2n + o(n) bits. It also supports efficient level-order traversal, a useful ordering previously supported only with a very limited set of operations (8).

Our second contribution expands on the notion of a single succinct representation supporting more than one traversal ordering, by showing that our method supports two other encoding schemes as abstract data types. In particular, it supports extracting a word (\(O(\lg n)\) bits) of the balanced parenthesis sequence (11) or depth first unary degree sequence (3;4) in O(f(n)) time, using at most n/f(n) + o(n) additional bits, for any f(n) in \(O(\lg n)\) and Ω(1).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Meng He
    • 1
  • J. Ian Munro
    • 1
  • S. Srinivasa Rao
    • 2
  1. 1.Cheriton School of Computer Science, University of WaterlooCanada
  2. 2.Computational Logic and Algorithms Group, IT University of CopenhagenDenmark

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