Abstract
Given a string X[1, n] and a position k in [1, n], the Shortest Unique Substring of X covering k, denoted by S_k, is a substring X[i, j] of X which satisfies the following conditions: (i) i leq k leq j, (ii) i is the only position where there is an occurrence of X[i, j], and (iii) j  i is minimized. The bestknown algorithm [Hon et al., ISAAC 2015] can find S k for all k in [1, n] in time O(n) using the string X and additional 2n words of working space. Let tau be a given parameter. We present the following new results. For any given k in [1, n], we can compute S_k via a deterministic algorithm in O(n tau^2 log n tau) time using X and additional O(n/tau) words of working space. For every k in [1, n], we can compute S_k via a deterministic algorithm in O(n tau^2 log n/tau) time using X and additional O(n/tau) words and 4n + o(n) bits of working space. For both problems above, we present an O(n tau log^{c+1} n)time randomized algorithm that uses n/ log c n words in addition to that mentioned above, where c geq 0 is an arbitrary constant. In this case, the reported string is unique and covers k, but with probability at most n^{O(1)} , may not be the shortest. As a consequence of our techniques, we also obtain similar spaceandtime tradeoffs for a related problem of finding Maximal Unique Matches of two strings [Delcher et al., Nucleic Acids Res. 1999].
BibTeX  Entry
@InProceedings{ganguly_et_al:LIPIcs:2016:6804,
author = {Arnab Ganguly and WingKai Hon and Rahul Shah and Sharma V. Thankachan},
title = {{SpaceTime TradeOffs for the Shortest Unique Substring Problem}},
booktitle = {27th International Symposium on Algorithms and Computation (ISAAC 2016)},
pages = {34:134:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770262},
ISSN = {18688969},
year = {2016},
volume = {64},
editor = {SeokHee Hong},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/6804},
URN = {urn:nbn:de:0030drops68041},
doi = {10.4230/LIPIcs.ISAAC.2016.34},
annote = {Keywords: Suffix Tree, Sparsification, RabinKarp Fingerprint, Probabilistic zFast Trie, Succinct DataStructures}
}
Keywords: 

Suffix Tree, Sparsification, RabinKarp Fingerprint, Probabilistic zFast Trie, Succinct DataStructures 
Collection: 

27th International Symposium on Algorithms and Computation (ISAAC 2016) 
Issue Date: 

2016 
Date of publication: 

07.12.2016 