A set of strings, called a string dictionary, is a basic string data structure. The most primitive query, where one seeks the existence of a pattern in the dictionary, is called a lookup query. Approximate lookup queries, i.e., to lookup the existence of a pattern with a bounded number of errors, is a fundamental string problem. Several data structures have been proposed to do so efficiently. Almost all solutions consider a single error, as will this result. Lately, Belazzougui and Venturini (CPM 2013) raised the question whether one can construct efficient indexes that support lookup queries with one error in optimal query time, that is, O(|p|/ω + occ), where p is the query, ω the machine word-size, and occ the number of occurrences. Specifically, for the problem of one mismatch and constant alphabet size, we obtain optimal query time. For a dictionary of d strings our proposed index uses O(ωd log1+ε d) additional bit space (beyond the space required to access the dictionary data, which can be maintained in compressed form). Our results are parameterized for a space-time tradeoff. We propose more results for the case of lookup queries with one insertion/ deletion on dictionaries over a constant sized alphabet. These results are especially effective for large patterns.
|Title of host publication||Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings|
|Editors||Ugo Vaccaro, Ely Porat, Ferdinando Cicalese|
|Number of pages||10|
|State||Published - 2015|
|Event||26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015 - Ischia Island, Italy|
Duration: 29 Jun 2015 → 1 Jul 2015
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015|
|Period||29/06/15 → 1/07/15|
Bibliographical noteFunding Information:
M. Lewenstein—This research is supported by a BSF grant 2010437 and a GIF grant 1147/2011.
T. Chan—The research is supported by an NSERC grant.
© Springer International Publishing Switzerland 2015.