Efficient Compressed Representation of Repetitive Texts with Direct Access

Grunnleggende konsepter

Generalized Straight-Line Programs (GSLPs) can be balanced to have height O(log n) without asymptotically increasing their size. Iterated SLPs (ISLPs), a specialized form of GSLPs, can represent some text families in size o(δ) while supporting efficient substring extraction and other queries.

Sammendrag

The content discusses the development of a new class of grammars called Generalized Straight-Line Programs (GSLPs) that can be efficiently balanced without increasing their asymptotic size. GSLPs extend traditional Straight-Line Programs (SLPs) by allowing special rules of the form A→x, where x is a program (in any Turing-complete language) that outputs a sequence of variables.

The authors then introduce a specialized form of GSLPs called Iterated SLPs (ISLPs), which allow more complex iteration rules of the form A→Πk2i=k1Bic1
1 ... Bict
t. They show that ISLPs can represent some text families in size o(δ), where δ is a lower-bounding measure of repetitiveness, while still supporting efficient substring extraction and other queries.

Specifically:

• The authors prove that any balanceable GSLP can be transformed into an equivalent GSLP of the same asymptotic size but with a derivation tree of height O(log n).
• They introduce ISLPs, a specialized form of GSLPs, and show that some text families can be represented by an ISLP of size O(δ/√n), breaking the Ω(δ) barrier.
• Using the balancing property of GSLPs, they show that ISLPs can extract any substring of length λ in time O(λ + log^2 n log log n), as well as compute various substring queries in time O(log^2 n log log n).
• They further specialize ISLPs to Run-Length SLPs (RLSLPs), and show how to efficiently compute a wide class of "composable" substring queries, such as Karp-Rabin fingerprints, in time O(log n).

Statistikk

There are no key metrics or important figures used to support the author's key logics.

Sitater

There are no striking quotes supporting the author's key logics.

Viktige innsikter hentet fra

Generalized Straight-Line Programs

by Gonzalo Nava... klokken arxiv.org 04-11-2024

https://arxiv.org/pdf/2404.07057.pdf

Dypere Spørsmål

How can the balancing technique for GSLPs be extended or applied to other grammar-based compression schemes beyond SLPs and ISLPs

The balancing technique for GSLPs can be extended and applied to other grammar-based compression schemes beyond SLPs and ISLPs by considering the structural similarities and differences between different types of grammars. One approach could be to adapt the balancing algorithm to work with the specific rules and constraints of the target grammar format. For example, if we consider context-free grammars or other types of grammar systems, we can analyze the rules and transformations involved in balancing SLPs and ISLPs and modify them to suit the requirements of the new grammar format. By understanding the underlying principles of grammar compression and the balancing process, we can potentially develop similar techniques for a broader range of grammar-based compression schemes.

Are there other specialized forms of GSLPs, beyond ISLPs, that can further improve the size-time tradeoffs for compressed text representations

There are indeed other specialized forms of GSLPs that can further improve the size-time tradeoffs for compressed text representations. One such specialization could involve incorporating additional constraints or optimizations in the grammar rules to enhance compression efficiency. For example, introducing specific rules for handling repetitive patterns or optimizing the representation of common substrings can lead to more compact and faster-to-access compressed text representations. By tailoring the GSLPs to the characteristics of the text data, such as its repetitiveness or specific patterns, we can create specialized grammar structures that offer improved compression ratios and faster query processing capabilities.

What are the practical implications and potential applications of the efficient substring extraction and query capabilities provided by the balanced ISLP and RLSLP representations

The efficient substring extraction and query capabilities provided by the balanced ISLP and RLSLP representations have several practical implications and potential applications in various fields. One key application is in data storage and retrieval systems where large volumes of text data need to be compressed for efficient storage and quick access. By using ISLPs and RLSLPs, organizations can significantly reduce the storage space required for text data while still being able to access and manipulate the data efficiently. This can lead to cost savings and improved performance in applications such as search engines, databases, and archival systems. Additionally, the ability to perform substring queries quickly and accurately opens up possibilities for advanced text processing tasks such as pattern matching, data mining, and information retrieval, enabling more sophisticated analysis and extraction of information from compressed text data.