A cover of a string S is a string C such that every index of S is contained in some occurrence of C. First introduced by Apostolico and Ehrenfeucht [TCS'93] over 30 years ago, covers have since received significant attention in the string algorithms community. In this work, we present a space-efficient algorithm for computing a compact representation of all covers of a given string. Our algorithm requires only O(log n) additional memory while accessing the input string of length n in a read-only manner. Moreover, it runs in O(n) time, matching the best-known time complexity for this problem while achieving an exponential improvement in space usage.
@InProceedings{boneh_et_al:LIPIcs.CPM.2025.5, author = {Boneh, Itai and Golan, Shay}, title = {{Covers in Optimal Space}}, booktitle = {36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)}, pages = {5:1--5:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-369-0}, ISSN = {1868-8969}, year = {2025}, volume = {331}, editor = {Bonizzoni, Paola and M\"{a}kinen, Veli}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.5}, URN = {urn:nbn:de:0030-drops-230993}, doi = {10.4230/LIPIcs.CPM.2025.5}, annote = {Keywords: Cover, Read-only random access, small space} }
Feedback for Dagstuhl Publishing