On Extensions of Maximal Repeats in Compressed Strings

02/14/2020

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by   Julian Pape-Lange, et al.

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This paper provides an upper bound for several subsets of maximal repeats and maximal pairs in compressed strings and also presents a formerly unknown relationship between maximal pairs and the run-length Burrows-Wheeler transform. This relationship is used to obtain a different proof for the Burrows-Wheeler conjecture which has recently been proven by Kempa and Kociumaka in "Resolution of the Burrows-Wheeler Transform Conjecture". More formally, this paper proves that a string S with z LZ77-factors and without q-th powers has at most 73(log_2 |S|)(z+2)^2 runs in the run-length Burrows-Wheeler transform and the number of arcs in the compacted directed acyclic word graph of S is bounded from above by 18q(1+log_q |S|)(z+2)^2.