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Linked Dynamic Tries with Applications to LZ-Compression in Sublinear Time and Space

Jesper Jansson, Kunihiko Sadakane, Wing-Kin Sung
2013 Algorithmica  
The dynamic trie is a fundamental data structure with applications in many areas of computer science.  ...  Our method is not only space-efficient, but also allows the longest common prefix between any query pattern P and the  ...  Acknowledgements The authors would like to thank the anonymous referees for their helpful comments.  ... 
doi:10.1007/s00453-013-9836-6 fatcat:oequ4anh5fgyfexdltisqikwku

Compressed Dynamic Tries with Applications to LZ-Compression in Sublinear Time and Space [chapter]

Jesper Jansson, Kunihiko Sadakane, Wing-Kin Sung
2007 Lecture Notes in Computer Science  
Compressed Dynamic Tries with Applications to LZ-Compression 425 computer networks, dynamic tries are used in IP routing to efficiently maintain the hierarchical organization of routing information to  ...  No previous algorithm runs in sublinear time. Our new data structure implies a LZ-compression algorithm which runs in sublinear time and uses optimal working space.  ...  By maintaining the lz-trie using our dynamic trie data structure, we obtain the first LZ compression algorithm which uses optimal working space and runs in sublinear time when σ = 2 o(log s log log log  ... 
doi:10.1007/978-3-540-77050-3_35 fatcat:qudoqejvrjdhjn6dflooqcemzm

Packed Compact Tries: A Fast and Efficient Data Structure for Online String Processing

Takuya TAKAGI, Shunsuke INENAGA, Kunihiko SADAKANE, Hiroki ARIMURA
2017 IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences  
We also discuss an application of our packed c-tries to online LZD factorization.  ...  , can be constructed online in O((n/α + k) f(k,n)) worst-case time and O(n/α + k f(k,n)) expected time with n σ + O(k n) bits of space.  ...  Using our packed c-tries, we achieve a good expected performance with O(k( M α + f (k, n))) time for LZDF. All the proofs omitted due to lack of space can be found in Appendix. Related work.  ... 
doi:10.1587/transfun.e100.a.1785 fatcat:oqtma2hqg5dylj5g7o73hcrfea

Approximate String Matching with Compressed Indexes

Luís M. Russo, Gonzalo Navarro, Arlindo Oliveira, Pedro Morales
2009 Algorithms  
A compressed full-text self-index for a text T is a data structure requiring reduced space and able to search for patterns P in T .  ...  We show experimentally that our algorithms are competitive and provide useful space-time tradeoffs compared to classical indexes.  ...  This can be easily found in time O(m 2 k) with (a different) dynamic programming [16] . However, we need to know the frequencies in the text of every pattern substring.  ... 
doi:10.3390/a2031105 fatcat:y5co44757jgi5eabwlslyutddu

Compressed Suffix Arrays and Suffix Trees with Applications to Text Indexing and String Matching

Roberto Grossi, Jeffrey Scott Vitter
2005 SIAM journal on computing (Print)  
Our result thus presents for the first time an efficient index whose size is provably linear in the size of the text in the worst case, and for many scenarios, the space is actually sublinear in practice  ...  Our theoretical bounds improve both time and space of previous indexing schemes.  ...  Before we discuss how to construct the index, we first need to show that search in Patricia tries, which normally proceeds one level at a time, can be improved to sublinear time by processing lg n bits  ... 
doi:10.1137/s0097539702402354 fatcat:272sxplz6jamrehddo2zbxdhxu

Indexed Hierarchical Approximate String Matching [chapter]

Luís M. S. Russo, Gonzalo Navarro, Arlindo L. Oliveira
2008 Lecture Notes in Computer Science  
We compare our algorithm with related approaches, showing that our method offers an interesting space/time tradeoff, and in particular does not need of any parameterization, which is necessary in the most  ...  This turns out to be easily supported by most compressed text self-indexes, which represent the index and the text essentially in the same space of the compressed text alone.  ...  Although it was less efficient than the ILZI-based algorithm, it requires less space in theory and in practice.  ... 
doi:10.1007/978-3-540-89097-3_15 fatcat:qyyznrzfmnd4bcthjq4bkaonwa

String Pattern Matching for a Deluge Survival Kit [chapter]

Alberto Apostolico, Maxime Crochemore
2002 Massive Computing  
In massive applications, even time O(kn) may be prohibitive. Using filtration methods it is possible to set up sublinear expected time queries.  ...  However, there are more efficient methods to deal with this restricted case. In fact, a time complexity O(kn) and even sublinear expected time are achievable.  ... 
doi:10.1007/978-1-4615-0005-6_6 fatcat:zx3uoflljbfs7oyclwxk2ic2ua

Orthogonal Range Searching for Text Indexing [article]

Moshe Lewenstein
2013 arXiv   pre-print
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.  ...  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.  ...  Special thanks to Orgad, Rahul, Sharma and Yakov for numerous Skype conversations in which I learned more than can be contained within this monologue.  ... 
arXiv:1306.0615v1 fatcat:g4nztbapzna3bhuj2nazlyw6re

Document Retrieval on Repetitive String Collections [article]

Travis Gagie, Aleksi Hartikainen, Kalle Karhu, Juha Kärkkäinen, Gonzalo Navarro, Simon J. Puglisi, Jouni Sirén
2017 arXiv   pre-print
As these collections keep growing, a key approach to handling them is to exploit their repetitiveness, which can reduce their space usage by orders of magnitude.  ...  We study the problem of indexing repetitive string collections in order to perform efficient document retrieval operations on them.  ...  Acknowledgements This work was supported in part by Academy of Finland grants 268324, 258308, 250345 (CoECGR), and 134287; the Helsinki Doctoral Programme in Computer Science; the Jenny and Antti Wihuri  ... 
arXiv:1605.09362v3 fatcat:goqxqemkdzfyrgffkbhr44nrja

Document retrieval on repetitive string collections

Travis Gagie, Aleksi Hartikainen, Kalle Karhu, Juha Kärkkäinen, Gonzalo Navarro, Simon J. Puglisi, Jouni Sirén
2017 Information retrieval (Boston)  
As these collections keep growing, a key approach to handling them is to exploit their repetitiveness, which can reduce their space usage by orders of magnitude.  ...  Finally, we show how the tools we Preliminary partial versions of this paper appeared in developed can be combined to solve ranked conjunctive and disjunctive multi-term queries under the simple tf-idf  ...  PDL with storing factor b set was between Brute-L and Brute-D in both time and space.  ... 
doi:10.1007/s10791-017-9297-7 pmid:28596702 pmcid:PMC5445192 fatcat:uiju2twyyvetpgs355f5srn2ui

Compressed full-text indexes

Gonzalo Navarro, Veli Mäkinen
2007 ACM Computing Surveys  
The most successful indexes nowadays are able to obtain almost optimal space and search time simultaneously. In this paper we present the main concepts underlying (compressed) self-indexes.  ...  The exciting possibility of an index that takes space close to that of the compressed text, replaces it, and in addition provides fast search over it, has triggered a wealth of activity and produced surprising  ...  Acknowledgements We thank Paolo Ferragina, Kunihiko Sadakane, and the anonymous referees for their invaluable help to improve this survey. Their hard work is greatly appreciated.  ... 
doi:10.1145/1216370.1216372 fatcat:cvpuqe5kl5gibfa6xvqvhg3kaa

Indexing Highly Repetitive String Collections [article]

Gonzalo Navarro
2022 arXiv   pre-print
Two decades ago, a breakthrough in indexing string collections made it possible to represent them within their compressed space while at the same time offering indexed search functionalities.  ...  As this new technology permeated through applications like bioinformatics, the string collections experienced a growth that outperforms Moore's Law and challenges our ability of handling them even in compressed  ...  We will use big-O notation for the time complexities, and in many cases for the space complexities as well.  ... 
arXiv:2004.02781v9 fatcat:rceyc6ti5jdfpebkrbbgq3kine

Data compression in dynamic systems

Su Chen
2008
We introduce new Haar wavelet synopsis for nonuniform accuracy and time-varying data that can be generated in near linear time and space, and updated in sublinear time.  ...  Data compression in dynamic systems has several applications in the real world. Unlike the compression of static data, both data and intrinsic data patterns may change over time.  ...  We introduce new Haar wavelet synopsis for nonuniform accuracy and time-varying data that can be generated in near linear time and space, and updated in sublinear time.  ... 
doi:10.7282/t3q81dg0 fatcat:whpkuzzyczaa7owszaqw6mgjoa

Exploring regular structures in strings

Dominik Köppl, Technische Universität Dortmund, Technische Universität Dortmund
2018
This thesis is dedicated to string processing algorithms and to combinatorics on words. With respect to the former, we devise Lempel-Ziv (LZ) factorization and sparse suffix sorting algorithms.  ...  The results can contribute to tools for data compression, for text indexing, and for the analysis of biological sequences.  ...  within compressed space and in near-linear time, which is not possible (to date) for LZ77.  ... 
doi:10.17877/de290r-19051 fatcat:sqgkahsn35dzfejuxrgn2zqdt4

The International Symposium on Advances in Content-oriented Networks and Systems CONNET 2015 Technical Program Committee

Tao Zheng, Carlos Westphall, Pedro Andrés, Aranda Gutiérrez, Telefónica I+d -Madrid, Spain Carlos, Becker Westphall, Simone Silvestri, Yoshiaki Taniguchi, Abdulrahman Yarali, Emmanuel Bertin, Steffen Fries (+201 others)
unpublished
Packet Dynamics refers broadly to measurements, theory and/or models that describe the time evolution and the associated attributes of packets, flows or streams of packets in a network.  ...  With the growth of the Internet in size, speed and traffic volume, understanding the impact of underlying network resources and protocols on packet delivery and application performance has assumed a critical  ...  Our system uses Easyhook to inject the preestablished data link layer or Dynamic Link Library (DLL) into every application's memory space.  ... 
fatcat:jwpmtq52cvajxesuwhilcta6ny
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