Succinct Ordinal Trees Based on Tree Covering

Abstract. Various methods have been used to represent a tree on n nodes in essentially the informationtheoretic 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. [8], 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 [10]. Our second contribution expands on the notion of a single succinct representation supporting more than ersal 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)4 of the balanced parenthesis sequence [13] or depth first unary degree sequence [4] in O(f(n))...

• Type: Conference
• Year: 2007
• Where: ICALP
• Authors: Meng He, J. Ian Munro, S. Srinivasa Rao
• Keywords: ICALP 2007, Navigational Operations, Succinct Representation, Theoretical Computer Science, Various Navigational Operations