Dynamic Relative Compression, Dynamic Partial Sums, and Substring Concatenation

Given a static reference string R and a source string S , a relative compression of S with respect to R is an encoding of S as a sequence of references to substrings of R . Relative compression schemes are a classic model of compression and have recently proved very successful for compressing highly...

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Vydané v:Algorithmica Ročník 80; číslo 11; s. 3207 - 3224
Hlavní autori: Bille, Philip, Christiansen, Anders Roy, Cording, Patrick Hagge, Gørtz, Inge Li, Skjoldjensen, Frederik Rye, Vildhøj, Hjalte Wedel, Vind, Søren
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.11.2018
Springer Nature B.V
Predmet:
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Data compression
Data structures
Data Structures and Information Theory
Genomes
Mathematics of Computing
Pattern matching
Random access
Sums
Theory of Computation
Partial Sums Problem
Reference String
Substring Concatenation
Source String
Relative Compression
ISSN:0178-4617, 1432-0541
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Popis
Shrnutí:Given a static reference string R and a source string S , a relative compression of S with respect to R is an encoding of S as a sequence of references to substrings of R . Relative compression schemes are a classic model of compression and have recently proved very successful for compressing highly-repetitive massive data sets such as genomes and web-data. We initiate the study of relative compression in a dynamic setting where the compressed source string S is subject to edit operations. The goal is to maintain the compressed representation compactly, while supporting edits and allowing efficient random access to the (uncompressed) source string. We present new data structures that achieve optimal time for updates and queries while using space linear in the size of the optimal relative compression, for nearly all combinations of parameters. We also present solutions for restricted and extended sets of updates. To achieve these results, we revisit the dynamic partial sums problem and the substring concatenation problem. We present new optimal or near optimal bounds for these problems. Plugging in our new results we also immediately obtain new bounds for the string indexing for patterns with wildcards problem and the dynamic text and static pattern matching problem.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-017-0380-7