Practical approaches to reduce the space requirement of lempel-ziv--based compressed text indices

Abstract

Given a text T [1¨ n ] over an alphabet of size σ, the full-text search problem consists in locating the occ occurrences of a given pattern P [1¨ m ] in T . Compressed full-text self-indices are space-efficient representations of the text that provide direct access to and indexed search on it. The LZ-index of Navarro is a compressed full-text self-index based on the LZ78 compression algorithm. This index requires about 5 times the size of the compressed text (in theory, 4 nH k ( T )+ o ( n logσ) bits of space, where H k ( T ) is the k -th order empirical entropy of T ). In practice, the average locating complexity of the LZ-index is O (σ m log σ n + occ σ m /2), where occ is the number of occurrences of P . It can extract text substrings of length ℓ in O (ℓ) time. This index outperforms competing schemes both to locate short patterns and to extract text snippets. However, the LZ-index can be up to 4 times larger than the smallest existing indices (which use nH k ( T )+ o ( n logσ) bits in theory), and it does not offer space/time tuning options. This limits its applicability. In this article, we study practical ways to reduce the space of the LZ-index. We obtain new LZ-index variants that require 2(1+ϵ) nH k ( T ) + o ( n logσ) bits of space, for any 0<ϵ <1. They have an average locating time of O (1/ϵ( m log n + occ σ m /2 )), while extracting takes O (ℓ) time. We perform extensive experimentation and conclude that our schemes are able to reduce the space of the original LZ-index by a factor of 2/3, that is, around 3 times the compressed text size. Our schemes are able to extract about 1 to 2 MB of the text per second, being twice as fast as the most competitive alternatives. Pattern occurrences are located at a rate of up to 1 to 4 million per second. This constitutes the best space/time trade-off when indices are allowed to use 4 times the size of the compressed text or more.