The Internet Archive has a preservation copy of this work in our general collections.
The file type is `application/pdf`

.

## Filters

##
###
Data Structure Lower Bounds on Random Access to Grammar-Compressed Strings
[article]

2012
*
arXiv
*
pre-print

All of our

arXiv:1203.1080v2
fatcat:fjfenk2vzvfh7mev5okt4ce4i4
*lower**bounds*hold even when the*strings*are over an alphabet of size 2 and hold even for*randomized**data**structures*with 2-sided error. ... In this paper we investigate the problem of building a static*data**structure*that represents a*string*s using space close*to*its*compressed*size, and allows fast*access**to*individual characters of s. ...*Lower**Bound*for*Grammar**Random**Access*In this section we prove the main*lower**bound*for*grammar**random**access*. In Section 3.1 we show the main reduction from SD and BLSD. ...##
###
Data Structure Lower Bounds on Random Access to Grammar-Compressed Strings
[chapter]

2013
*
Lecture Notes in Computer Science
*

All of our

doi:10.1007/978-3-642-38905-4_24
fatcat:kywb33jslzbrrblpblangd5bz4
*lower**bounds*hold even when the*strings*are over an alphabet of size 2 and hold even for*randomized**data**structures*with 2-sided error. ... In this paper we investigate the problem of building a static*data**structure*that represents a*string*s using space close*to*its*compressed*size, and allows fast*access**to*individual characters of s. ...*Lower**Bound*for*Grammar**Random**Access*In this section we prove the main*lower**bound*for*grammar**random**access*. In Section 3.1 we show the main reduction from SD and BLSD. ...##
###
Optimal Time Random Access to Grammar-Compressed Strings in Small Space
[article]

2015
*
arXiv
*
pre-print

The

arXiv:1410.4701v4
fatcat:o5cm5u4o25hjvmocdisycjv6hi
*random**access*problem for*compressed**strings*is*to*build a*data**structure*that efficiently supports*accessing*the character in position $i$ of a*string*given in*compressed*form. ... Given a*grammar*of size $n$*compressing*a*string*of size $N$, we present a*data**structure*using $O(n\Delta \log_\Delta \frac N n \log N)$ bits of space that supports*accessing*position $i$ in $O(\log_\ ... The*random**access*problem*on**grammar*-*compressed**strings*is*to*build a*data**structure*that efficiently supports*accessing*S[i]. ...##
###
Balancing Straight-Line Programs for Strings and Trees
[chapter]

2020
*
Lecture Notes in Computer Science
*

The talk will explain a recent balancing result according

doi:10.1007/978-3-030-51466-2_26
fatcat:dwou7yn7cfhuzooctunvaw6pme
*to*which a context-free*grammar*in Chomsky normal form of size m that produces a single*string*w of length n (such a*grammar*is also called a straight-line ... Similar balancing results can be formulated for various*grammar*-based tree*compression*formalism like top DAGs and forest straight-line programs. ... We can also obtain an algorithm for the*random**access*problem with*access*time O(log n/log log n) using a*data**structure*with O(m · log n) words for any > 0; previously this*bound*was only shown for SLPs ...##
###
Finger Search in Grammar-Compressed Strings
[article]

2016
*
arXiv
*
pre-print

*Grammar*-based

*compression*, where

*one*replaces a long

*string*by a small context-free

*grammar*that generates the

*string*, is a simple and powerful paradigm that captures many popular

*compression*schemes. ... Given a

*grammar*, the

*random*

*access*problem is

*to*compactly represent the

*grammar*while supporting

*random*

*access*, that is, given a position in the original uncompressed

*string*report the character at that ... The

*random*

*access*problem is

*one*of the most basic primitives for computation

*on*

*grammar*

*compressed*

*strings*, and solutions

*to*the problem are a key component in a wide range of algorithms and

*data*

*structures*...

##
###
Finger Search in Grammar-Compressed Strings

2018
*
Theory of Computing Systems
*

*Grammar*-based

*compression*, where

*one*replaces a long

*string*by a small context-free

*grammar*that generates the

*string*, is a simple and powerful paradigm that captures many popular

*compression*schemes. ... Given a

*grammar*, the

*random*

*access*problem is

*to*compactly represent the

*grammar*while supporting

*random*

*access*, that is, given a position in the original uncompressed

*string*report the character at that ... The

*random*

*access*problem is

*one*of the most basic primitives for computation

*on*

*grammar*

*compressed*

*strings*, and solutions

*to*the problem are a key component in a wide range of algorithms and

*data*

*structures*...

##
###
Practical Random Access to SLP-Compressed Texts
[article]

2020
*
arXiv
*
pre-print

so attractive: the possibility of supporting fast

arXiv:1910.07145v4
fatcat:rbhejzignnaariowaosidwwzr4
*random**access*. ... In a recent paper (SPIRE 2019) we showed how simple pre-processing can dramatically improve those trade-offs, and in this paper we turn our attention*to**one*of the features that make*grammar*-based*compression*... Prezza [27] sidestepped Verbin and Yu's*lower**bound**to*obtain constant-time*random**access**to*T with an O(gn )-space*grammar*(after Belazzougui et al. [3] achieved that tradeoff with block trees). ...##
###
Optimal Rank and Select Queries on Dictionary-Compressed Text
[article]

2018
*
arXiv
*
pre-print

Recent works showed that

arXiv:1811.01209v3
fatcat:pxqxwc3dkrhm7l3bsopwr4jgue
*random**access**on*S can be supported in optimal O((n/γ)/ n) time within O (γ polylog n ) space. ... We also provide matching*lower*and upper*bounds*for partial sum and predecessor queries within attractor-*bounded*space, and extend our*lower**bounds**to*encompass navigation of dictionary-*compressed*tree ... Any static*data**structure*taking O(g polylog n) space cannot answer*random**access*queries*on*S in less than O(log n/ log log n) time. ...##
###
A Succinct Grammar Compression
[article]

2013
*
arXiv
*
pre-print

We solve an open problem related

arXiv:1304.0917v3
fatcat:y4ys7rg2zjelhktsvjwjowg2sa
*to*an optimal encoding of a straight line program (SLP), a canonical form of*grammar**compression*deriving a single*string*deterministically. ... The space is at most 2n log rho(1 + o(1)) bits for rho leq 2sqrtn, while supporting*random**access**to*any production rule of an SLP in O(log log n) time. ... Such a*data**structure*is called a naming function, and is also necessary for practical*grammar**compressions*. ...##
###
A Simple Online Competitive Adaptation of Lempel-Ziv Compression with Efficient Random Access Support

2013
*
2013 Data Compression Conference
*

We present a simple adaptation of the Lempel Ziv 78' (LZ78)

doi:10.1109/dcc.2013.19
dblp:conf/dcc/DuttaLRR13
fatcat:fcnf4rtjhvcynhlv42fanvceey
*compression*scheme (IEEE Transactions*on*Information Theory, 1978) that supports efficient*random**access**to*the input*string*. ... Namely, given query*access**to*the*compressed**string*, it is possible*to*efficiently recover any symbol of the input*string*. ... We would like*to*thank Giuseppe Ottaviano for a helpful discussion and two anonymous referees for their constructive comments. ...##
###
A Succinct Grammar Compression
[chapter]

2013
*
Lecture Notes in Computer Science
*

We solve an open problem related

doi:10.1007/978-3-642-38905-4_23
fatcat:svy5obmutbc6lb3jp4dddskeim
*to*an optimal encoding of a straight line program (SLP), a canonical form of*grammar**compression*deriving a single*string*deterministically. ... The space is at most 2n log ρ(1 + o(1)) bits for ρ ≤ 2 √ n, while supporting*random**access**to*any production rule of an SLP in O(log log n) time. ... Such a*data**structure*is called a naming function, and is also necessary for practical*grammar**compressions*. ...##
###
Random Access to Grammar Compressed Strings
[article]

2013
*
arXiv
*
pre-print

*To*achieve these

*bounds*, we introduce several new techniques and

*data*

*structures*of independent interest, including a predecessor

*data*

*structure*, two "biased" weighted ancestor

*data*

*structures*, and a compact ... In this paper, we present a novel

*grammar*representation that allows efficient

*random*

*access*

*to*any character or substring without decompressing the

*string*. ... approximate matching

*grammar*

*compressed*

*strings*(giving the

*bounds*of Theorem 2). ...

##
###
Page 716 of Mathematical Reviews Vol. , Issue 2001A
[page]

2001
*
Mathematical Reviews
*

Summary: “We investigate a type of lossless source code called a

*grammar*-based code, which, in response*to*any input*data**string*x over a fixed finite alphabet, selects a context-free*grammar*G, representing ... Redun- dancy*bounds*for*grammar*-based codes are established. ...##
###
Rank, select and access in grammar-compressed strings
[article]

2014
*
arXiv
*
pre-print

In this paper we describe

arXiv:1408.3093v2
fatcat:swad75hy3zcthfwtwagmvte7we
*data**structures**to*support the following operations*on*a*grammar*-*compressed**string*: rank_c(S,i) (return the number of occurrences of symbol c before position i in S); select_c ... This matches a*lower**bound*stated by Verbin and Yu for*strings*where N is polynomially related*to*n. ... We note that our upper*bound*for*access*matches the*lower**bound*of Verbin and Yu [48] who have shown that for "not-so-*compressible*"*strings*-those that have a*grammar*of length n such that N ≤ n 1+ for ...##
###
A simple online competitive adaptation of Lempel-Ziv compression with efficient random access support
[article]

2013
*
arXiv
*
pre-print

We present a simple adaptation of the Lempel Ziv 78' (LZ78)

arXiv:1301.2495v1
fatcat:fjpeikjhz5bwnfz7txl7wyepnu
*compression*scheme ( IEEE Transactions*on*Information Theory, 1978) that supports efficient*random**access**to*the input*string*. ... Namely, given query*access**to*the*compressed**string*, it is possible*to*efficiently recover any symbol of the input*string*. ... We would like*to*thank Giuseppe Ottaviano for a helpful discussion and two anonymous referees for their constructive comments. ...
« Previous

*Showing results 1 — 15 out of 2,165 results*