TY - GEN
T1 - Novel Results on the Number of Runs of the Burrows-Wheeler-Transform
AU - Giuliani, Sara
AU - Inenaga, Shunsuke
AU - Lipták, Zsuzsanna
AU - Prezza, Nicola
AU - Sciortino, Marinella
AU - Toffanello, Anna
N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
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U2 - 10.1007/978-3-030-67731-2_18
DO - 10.1007/978-3-030-67731-2_18
M3 - Conference contribution
AN - SCOPUS:85101538030
SN - 9783030677305
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 249
EP - 262
BT - SOFSEM 2021
A2 - Bureš, Tomáš
A2 - Dondi, Riccardo
A2 - Gamper, Johann
A2 - Guerrini, Giovanna
A2 - Jurdzinski, Tomasz
A2 - Pahl, Claus
A2 - Sikora, Florian
A2 - Wong, Prudence W.
PB - Springer Science and Business Media Deutschland GmbH
T2 - 47th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2021
Y2 - 25 January 2021 through 29 January 2021
ER -