Succinct ordinal trees with level-ancestor queries

Abstract

We consider succinct or space-efficient representations of trees that efficiently support a variety of navigation operations. We focus on static ordinal trees, that is, 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 1989; Munro and Raman 2001; Benoit et al. 1999] to which we add the level-ancestor operation.Our representation takes 2 n + 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.