Novel Results on the Number of Runs of the Burrows-Wheeler-Transform

Sara Giuliani, Shunsuke Inenaga, Zsuzsanna Lipták, Nicola Prezza, Marinella Sciortino, Anna Toffanello

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

抄録

The Burrows-Wheeler-Transform (BWT), a reversible string transformation, is one of the fundamental components of many current data structures in string processing. It is central in data compression, as well as in efficient query algorithms for sequence data, such as webpages, genomic and other biological sequences, or indeed any textual data. The BWT lends itself well to compression because its number of equal-letter-runs (usually referred to as r) is often considerably lower than that of the original string; in particular, it is well suited for strings with many repeated factors. In fact, much attention has been paid to the r parameter as measure of repetitiveness, especially to evaluate the performance in terms of both space and time of compressed indexing data structures. In this paper, we investigate ρ(v), the ratio of r and of the number of runs of the BWT of the reverse of v. Kempa and Kociumaka [FOCS 2020] gave the first non-trivial upper bound as ρ(v) = O(log 2(n) ), for any string v of length n. However, nothing is known about the tightness of this upper bound. We present infinite families of binary strings for which ρ(v) = Θ(log n) holds, thus giving the first non-trivial lower bound on ρ(n), the maximum over all strings of length n. Our results suggest that r is not an ideal measure of the repetitiveness of the string, since the number of repeated factors is invariant between the string and its reverse. We believe that there is a more intricate relationship between the number of runs of the BWT and the string’s combinatorial properties.

本文言語英語
ホスト出版物のタイトルSOFSEM 2021
ホスト出版物のサブタイトルTheory and Practice of Computer Science - 47th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2021, Proceedings
編集者Tomáš Bureš, Riccardo Dondi, Johann Gamper, Giovanna Guerrini, Tomasz Jurdzinski, Claus Pahl, Florian Sikora, Prudence W. Wong
出版社Springer Science and Business Media Deutschland GmbH
ページ249-262
ページ数14
ISBN(印刷版)9783030677305
DOI
出版ステータス出版済み - 2021
イベント47th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2021 - Bolzano-Bozen, イタリア
継続期間: 1 25 20211 29 2021

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
12607 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

会議

会議47th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2021
Countryイタリア
CityBolzano-Bozen
Period1/25/211/29/21

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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