Compressed Indexes for Aligned Pattern Matching

Thankachan, Sharma V.

doi:10.1007/978-3-642-24583-1_40

Cited by 3 publications

(3 citation statements)

References 15 publications

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“…By Bille and Gørtz' arguments, our results give linear space and time bounds for positionrestricted substring counting and the counting versions of indexing substrings with intervals and indexing substrings with gaps. We show they also imply linear space and time bounds for the counting version of aligned pattern matching [15].…”

Section: Introductionmentioning

confidence: 84%

“…For aligned pattern matching, we are given two strings S 1 and S 2 of total length n and asked to store them compactly such that later, given two patterns P 1 and P 2 of total length m, we can quickly find all the locations where P 1 occurs in S 1 and P 2 occurs in S 2 in the same position. Thankachan [15] noted that this problem can be solved directly via 2-dimensional range reporting, using O(n log n) space and O(log log n + t) time, where t is the number of such locations. He then showed how to store S 1 and S 2 in compressed form, but this solution takes O m + log 4+ n + t time when the lengths of P 1 and P 2 are both in Ω(log 2+ n), and…”

Section: Applicationsmentioning

confidence: 99%

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Linear-Space Substring Range Counting over Polylogarithmic Alphabets

Gagie,

Gawrychowski

2012

Preprint

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recently introduced the problem of substring range counting, for which we are asked to store compactly a string S of n characters with integer labels in [0, u], such that later, given an interval [a, b] and a pattern P of length m, we can quickly count the occurrences of P whose first characters' labels are in [a, b]. They showed how to store S in O(n log n/ log log n) space and answer queries in O(m + log log u) time. We show that, if S is over an alphabet of size polylog(n), then we can achieve optimal linear space. Moreover, if u = n polylog(n), then we can also reduce the time to O(m). Our results give linear space and time bounds for position-restricted substring counting and the counting versions of indexing substrings with intervals, indexing substrings with gaps and aligned pattern matching.

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Section: Introductionmentioning

confidence: 84%

Section: Applicationsmentioning

confidence: 99%

Linear-Space Substring Range Counting over Polylogarithmic Alphabets

Gagie,

Gawrychowski

2012

Preprint

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“…Another two lower bounds, along the lines of the lower bound described here, are for position restricted substring search [64], for forbidden patterns [51] and for aligned pattern matching [99].…”

Section: Lower Bounds On Text Indexing Via Range Reportingmentioning

confidence: 99%

Orthogonal Range Searching for Text Indexing

Lewenstein

2013

Lecture Notes in Computer Science

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Abstract. Text indexing, the problem in which one desires to preprocess a (usually large) text for future (shorter) queries, has been researched ever since the suffix tree was invented in the early 70's. With textual data continuing to increase and with changes in the way it is accessed, new data structures and new algorithmic methods are continuously required. Therefore, text indexing is of utmost importance and is a very active research domain. Orthogonal range searching, classically associated with the computational geometry community, is one of the tools that has increasingly become important for various text indexing applications. Initially, in the mid 90's there were a couple of results recognizing this connection. In the last few years we have seen an increase in use of this method and are reaching a deeper understanding of the range searching uses for text indexing. In this monograph we survey some of these results. moshe@cs.biu.ac.il. This paper was written while on Sabbatical in U. of Waterloo.

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