Efficient Index for Weighted Sequences

TY - CHAP

T1 - Efficient Index for Weighted Sequences

AU - Barton, Carl

AU - Kociumaka, Tomasz

AU - Pissis, Solon P.

AU - Radoszewski, Jakub

PY - 2016

Y1 - 2016

N2 - The problem of finding factors of a text string which are identical or similar to a given pattern string is a central problem in computer science. A generalised version of this problem consists in implementing an index over the text to support efficient on-line pattern queries. We study this problem in the case where the text is weighted: for every position of the text and every letter of the alphabet a probability of occurrence of this letter at this position is given. Sequences of this type, also called position weight matrices, are commonly used to represent imprecise or uncertain data. A weighted sequence may represent many different strings, each with probability of occurrence equal to the product of probabilities of its letters at subsequent positions. Given a probability threshold 1/z, we say that a pattern string P matches a weighted text at position i if the product of probabilities of the letters of P at positions i,...,i+|P|-1 in the text is at least 1/z. In this article, we present an O(nz)-time construction of an O(nz)-sized index that can answer pattern matching queries in a weighted text in optimal time improving upon the state of the art by a factor of z log z. Other applications of this data structure include an O(nz)-time construction of the weighted prefix table and an O(nz)-time computation of all covers of a weighted sequence, which improve upon the state of the art by the same factor.

AB - The problem of finding factors of a text string which are identical or similar to a given pattern string is a central problem in computer science. A generalised version of this problem consists in implementing an index over the text to support efficient on-line pattern queries. We study this problem in the case where the text is weighted: for every position of the text and every letter of the alphabet a probability of occurrence of this letter at this position is given. Sequences of this type, also called position weight matrices, are commonly used to represent imprecise or uncertain data. A weighted sequence may represent many different strings, each with probability of occurrence equal to the product of probabilities of its letters at subsequent positions. Given a probability threshold 1/z, we say that a pattern string P matches a weighted text at position i if the product of probabilities of the letters of P at positions i,...,i+|P|-1 in the text is at least 1/z. In this article, we present an O(nz)-time construction of an O(nz)-sized index that can answer pattern matching queries in a weighted text in optimal time improving upon the state of the art by a factor of z log z. Other applications of this data structure include an O(nz)-time construction of the weighted prefix table and an O(nz)-time computation of all covers of a weighted sequence, which improve upon the state of the art by the same factor.

U2 - 10.4230/LIPIcs.CPM.2016.4

DO - 10.4230/LIPIcs.CPM.2016.4

M3 - Conference paper

SN - 978-3-95977-012-5

VL - 54

T3 - Leibniz International Proceedings in Informatics (LIPIcs)

SP - 4:1-4:13

BT - 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)

A2 - Grossi, Roberto

A2 - Lewenstein, Moshe

PB - Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik

CY - Dagstuhl, Germany

ER -