Abstract
Given a string S, the compressed indexing problem is to preprocess S into a compressed representation that supports fast substring queries. The goal is to use little space relative to the compressed size of S while supporting fast queries. We present a compressed index based on the LempelZiv 1977 compression scheme. Let n, and z denote the size of the input string, and the compressed LZ77 string, respectively. We obtain the following timespace tradeoffs. Given a pattern string P of length m, we can solve the problem in
(i) O(m + occ lglg n) time using O(z lg(n/z) lglg z) space, or
(ii) O(m(1 + lg^e z / lg(n/z)) + occ(lglg n + lg^e z)) time using O(z lg(n/z)) space, for any 0 < e < 1
In particular, (i) improves the leading term in the query time of the previous best solution from O(m lg m) to O(m) at the cost of increasing the space by a factor lglg z. Alternatively, (ii) matches the previous best space bound, but has a leading term in the query time of O(m(1+lg^e z / lg(n/z))). However, for any polynomial compression ratio, i.e., z = O(n^{1d}), for constant d > 0, this becomes O(m). Our index also supports extraction of any substring of length l in O(l + lg(n/z)) time. Technically, our results are obtained by novel extensions and combinations of existing data structures of independent interest, including a new batched variant of weak prefix search.
BibTeX  Entry
@InProceedings{bille_et_al:LIPIcs:2017:7325,
author = {Philip Bille and Mikko Berggren Ettienne and Inge Li G\ortz and Hjalte Wedel Vildh\oj},
title = {{TimeSpace TradeOffs for LempelZiv Compressed Indexing}},
booktitle = {28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)},
pages = {16:116:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770392},
ISSN = {18688969},
year = {2017},
volume = {78},
editor = {Juha K{\"a}rkk{\"a}inen and Jakub Radoszewski and Wojciech Rytter},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7325},
URN = {urn:nbn:de:0030drops73254},
doi = {10.4230/LIPIcs.CPM.2017.16},
annote = {Keywords: compressed indexing, pattern matching, LZ77, prefix search}
}
Keywords: 

compressed indexing, pattern matching, LZ77, prefix search 
Collection: 

28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017) 
Issue Date: 

2017 
Date of publication: 

30.06.2017 