On the possible patterns of inputs for block sorting in the Burrows-Wheeler transformation

Authors:
Takashi Saso;Kojiro Kobayashi;Atsuyoshi Nakamura
Affiliations:
Graduate School of Engineering, Soka University, 1-236, Tangi-cho, Hachioji-shi, Tokyo, 192-8577, Japan;Graduate School of Engineering, Soka University, 1-236, Tangi-cho, Hachioji-shi, Tokyo, 192-8577, Japan;Graduate School of Information Science and Technology, Hokkaido University, Kita 14, Nishi 9, Kita-ku, Sapporo, Hokkaido, 060-0814, Japan
Venue:
Information Processing Letters
Year:
2011

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Abstract

Block sorting in the Burrows-Wheeler transformation is to sort all of the n circular shifts of a string of length n lexicographically. We introduce a notion called the width of a sequence of n strings of length n and show that the values of widths are very different between the two types of sequences of strings; (1) a sequence of n randomly generated strings of length n, and (2) the sequence of n circular shifts of a randomly generated string of length n.