This paper provides upper bounds 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 the run-length Burrows-Wheeler transform of a string S with z_S LZ77-factors has at most 73(log₂ |S|)(z_S+2)² runs, and if S does not contain q-th powers, the number of arcs in the compacted directed acyclic word graph of S is bounded from above by 18q(1+log_q |S|)(z_S+2)².
@InProceedings{papelange:LIPIcs.CPM.2020.27, author = {Pape-Lange, Julian}, title = {{On Extensions of Maximal Repeats in Compressed Strings}}, booktitle = {31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)}, pages = {27:1--27:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-149-8}, ISSN = {1868-8969}, year = {2020}, volume = {161}, editor = {G{\o}rtz, Inge Li and Weimann, Oren}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.27}, URN = {urn:nbn:de:0030-drops-121523}, doi = {10.4230/LIPIcs.CPM.2020.27}, annote = {Keywords: Maximal repeats, Extensions of maximal repeats, Combinatorics on compressed strings, LZ77, Burrows-Wheeler transform, Burrows-Wheeler transform conjecture, Compact suffix automata, CDAWGs} }
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