Dynamic Rank/Select Dictionaries with Applications to XML Indexing

We consider a central problem in text indexing: Given a text T over an alphabet Σ, construct a compressed data structure answering the queries char (i), rank s(i), and selects(i) for a symbol s ∈ Σ. Many data structures consider these queries for static text T [GGV03, FM01, SG06, GMR06]. We consider the dynamic version of the problem, where we are allowed to insert and delete symbols at arbitrary positions of T . This problem is a key challenge in compressed text indexing and has direct application to dynamic XML indexing structures that answer subpath queries [FLMM05]. We build on the results of [RRR02, GMR06] and give the best known query bounds for the dynamic version of this problem, supporting arbitrary insertions and deletions of symbols in T . Specifically, with an amortized update time of O((1/ )n ), we suggest how to support rank s(i), selects(i), and char (i) queries in O((1/ ) log log n) time, for any < 1. The best previous query times for this problem were O(log n log |Σ|), given by [MN06]. Our bounds are competitive with state-of-the-art static structures [GMR06]. Some applicable lower bounds for the partial sums problem [PD06] show that our update/query tradeoff is also nearly optimal. In addition, our space bound is competitive with the corresponding static structures. For the special case of bitvectors (i.e., |Σ| = 2), we also show the best tradeoffs for query/update time, improving upon the results of [MN06, HSS03, RRR02]. Finally, our focus on fast query/slower update is well-suited for a query-intensive XML indexing environment. Using the XBW transform [FLMM05], we also present a dynamic data structure that succinctly maintains an ordered labeled tree T and supports a powerful set of queries on T . ∗Department of Computer Sciences, Purdue University, West Lafayette, IN 47907–2066, USA ({agupta, wkhon, rahul}@cs.purdue.edu, [email protected]). 1