{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article9210","name":"Space-Time Trade-Offs for the Shortest Unique Substring Problem","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 best-known 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 space-and-time tradeoffs for a related problem of finding Maximal Unique Matches of two strings [Delcher et al., Nucleic Acids Res. 1999].","keywords":["Suffix Tree","Sparsification","Rabin-Karp Fingerprint","Probabilistic z-Fast Trie","Succinct Data-Structures"],"author":[{"@type":"Person","name":"Ganguly, Arnab","givenName":"Arnab","familyName":"Ganguly"},{"@type":"Person","name":"Hon, Wing-Kai","givenName":"Wing-Kai","familyName":"Hon"},{"@type":"Person","name":"Shah, Rahul","givenName":"Rahul","familyName":"Shah"},{"@type":"Person","name":"Thankachan, Sharma V.","givenName":"Sharma V.","familyName":"Thankachan"}],"position":34,"pageStart":"34:1","pageEnd":"34:13","dateCreated":"2016-12-07","datePublished":"2016-12-07","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Ganguly, Arnab","givenName":"Arnab","familyName":"Ganguly"},{"@type":"Person","name":"Hon, Wing-Kai","givenName":"Wing-Kai","familyName":"Hon"},{"@type":"Person","name":"Shah, Rahul","givenName":"Rahul","familyName":"Shah"},{"@type":"Person","name":"Thankachan, Sharma V.","givenName":"Sharma V.","familyName":"Thankachan"}],"copyrightYear":"2016","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.ISAAC.2016.34","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","citation":["http:\/\/dx.doi.org\/10.1007\/978-3-319-11918-2_18","http:\/\/dx.doi.org\/10.1007\/10719839_9","http:\/\/dx.doi.org\/10.1007\/3-540-45995-2_44","http:\/\/dx.doi.org\/10.1007\/978-3-662-48350-3_31","http:\/\/dx.doi.org\/10.1109\/SFCS.1997.646102","http:\/\/dx.doi.org\/10.1007\/978-3-540-74450-4_41","http:\/\/dx.doi.org\/10.1145\/828.1884","http:\/\/dx.doi.org\/10.1109\/DCC.2008.62","http:\/\/dx.doi.org\/10.1007\/978-3-662-48971-0_63","http:\/\/dx.doi.org\/10.1007\/978-3-319-07566-2_18","http:\/\/dx.doi.org\/10.1147\/rd.312.0249","http:\/\/dx.doi.org\/10.1002\/(SICI)1097-024X(199911)29:13<1149::AID-SPE274>3.0.CO;2-O","http:\/\/dx.doi.org\/10.1007\/3-540-62034-6_35","http:\/\/dx.doi.org\/10.1109\/ICDE.2013.6544887"],"isPartOf":{"@type":"PublicationVolume","@id":"#volume6267","volumeNumber":64,"name":"27th International Symposium on Algorithms and Computation (ISAAC 2016)","dateCreated":"2016-12-07","datePublished":"2016-12-07","editor":{"@type":"Person","name":"Hong, Seok-Hee","givenName":"Seok-Hee","familyName":"Hong"},"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article9210","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6267"}}}