The Wavelet Trie: Maintaining an Indexed Sequence of Strings in Compressed Space

摘要

An indexed sequence of strings is a data structure for storing a stringsequence that supports random access, searching, range counting and analyticsoperations, both for exact matches and prefix search. String sequences lie atthe core of column-oriented databases, log processing, and other storage andquery tasks. In these applications each string can appear several times and theorder of the strings in the sequence is relevant. The prefix structure of thestrings is relevant as well: common prefixes are sought in strings to extractinteresting features from the sequence. Moreover, space-efficiency is highlydesirable as it translates directly into higher performance, since more datacan fit in fast memory. We introduce and study the problem of compressed indexed sequence of strings,representing indexed sequences of strings in nearly-optimal compressed space,both in the static and dynamic settings, while preserving provably goodperformance for the supported operations. We present a new data structure for this problem, the Wavelet Trie, whichcombines the classical Patricia Trie with the Wavelet Tree, a succinct datastructure for storing a compressed sequence. The resulting Wavelet Triesmoothly adapts to a sequence of strings that changes over time. It improves onthe state-of-the-art compressed data structures by supporting a dynamicalphabet (i.e. the set of distinct strings) and prefix queries, both crucialrequirements in the aforementioned applications, and on traditional indexes byreducing space occupancy to close to the entropy of the sequence.