Compressing and indexing labeled trees, with applications

Abstract

Consider an ordered, static tree T where each node has a label from alphabet Σ. Tree T may be of arbitrary degree and shape. Our goal is designing a compressed storage scheme of T that supports basic navigational operations among the immediate neighbors of a node (i.e. parent, ith child, or any child with some label, . . .) as well as more sophisticated path-based search operations over its labeled structure.We present a novel approach to this problem by designing what we call the XBW-transform of the tree in the spirit of the well-known Burrows-Wheeler transform for strings [1994]. The XBW-transform uses path-sorting to linearize the labeled tree T into two coordinated arrays, one capturing the structure and the other the labels. For the first time, by using the properties of the XBW-transform, our compressed indexes support navigational and path-search operations over labeled trees within (near)-optimal time bounds and entropy-bounded space.Using the properties of the XBW-transform, we go beyond the information-theoretic lower bound. For the first time, our compressed indexes support navigational operations and path search operations within (near)-optimal time bounds and entropy-bounded space.Our XBW-transform is simple and likely to spur new results in the theory of tree compression and indexing, as well as interesting application contexts. As an example, we use the XBW-transform to design and implement a compressed index for XML documents whose compression ratio is significantly better than the one achievable by state-of-the-art tools, and its query time performance is order of magnitudes faster.

Tree Compression Using String Grammars

“…For unlabelled unranked trees of size n there exist representations with 2n + o(n) bits that support navigation and some other tree queries in time O(1) [6,23,24,36]. This result has been extended to labelled trees, where (log σ) · n + 2n + o(n) bits suffice when σ is the number of node labels [16].…”

Space efficient data structures for dynamic orthogonal range counting

“…This is because a (generalized) wavelet tree has, up to now, only been used to handle data of a two-dimensional nature for which the range of values in at least one dimension is fixed [6,5,3,7,8], such as sequences of integers from a fixed range in Theorem 1. To overcome this difficulty, our main strategy is to combine the notion of range trees [2] with generalized wavelet trees.…”

“…As succinct data structures provide solutions to modern applications that process large data sets, they have been studied extensively [14,6,5,7,3,8].…”

Top-k Substring Matching for Auto-Completion

“…First of all, we calculate [s s , e s ] = [8,10], the range of S such that the reverse prefixes starting with reversed Q "ba" and [s p , e p ] = [5,6], the range of the corresponding prefixes of P. P [5] has the highest score in P [5,6]. P [5] corresponds to S π [9]. The predecessors of S [9] are S [4], S [2] and S [1] (the root).…”