An encoding for order-preserving matching

Travis Gagie, Giovanni Manzini, Rossano Venturini

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Abstract

Encoding data structures store enough information to answer the queries they are meant to support but not enough to recover their underlying datasets. In this paper we give the first encoding data structure for the challenging problem of order-preserving pattern matching. This problem was introduced only a few years ago but has already attracted significant attention because of its applications in data analysis. Two strings are said to be an order-preserving match if the relative order of their characters is the same: E.g., 4, 1, 3, 2 and 10, 3, 7, 5 are an order preserving match. We show how, given a string S[1..n] over an arbitrary alphabet of size σ and a constant c ≥ 1, we can build an O(n log log n)-bit encoding such that later, given a pattern P[1..m] with m ≤ logcn, we can return the number of order-preserving occurrences of P in S in O(m) time. Within the same time bound we can also return the starting position of some order preserving match for P in S (if such a match exists). We prove that our space bound is within a constant factor of optimal if logσ=ω (log log n); our query time is optimal if logσ= (log n). Our space bound contrasts with the ω (n log n) bits needed in the worst case to store S itself, an index for order-preserving pattern matching with no restrictions on the pattern length, or an index for standard pattern matching even with restrictions on the pattern length. Moreover, we can build our encoding knowing only how each character compares to O(logc n) neighbouring characters.

Lingua originaleInglese
Titolo della pubblicazione ospite25th European Symposium on Algorithms, ESA 2017
EditorChristian Sohler, Christian Sohler, Kirk Pruhs
EditoreSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (elettronico)9783959770491
DOI
Stato di pubblicazionePubblicato - 1 set 2017
Pubblicato esternamente
Evento25th European Symposium on Algorithms, ESA 2017 - Vienna, Austria
Durata: 4 set 20176 set 2017

Serie di pubblicazioni

NomeLeibniz International Proceedings in Informatics, LIPIcs
Volume87
ISSN (stampa)1868-8969

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???event.eventtypes.event.conference???25th European Symposium on Algorithms, ESA 2017
Paese/TerritorioAustria
CittàVienna
Periodo4/09/176/09/17

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