Minimum Unique Substrings and Maximum Repeats

Authors:
Lucian Ilie;William F. Smyth
Affiliations:
(Correspd.) Department of Computer Science, University of Western Ontario, London ON N6A 5B7, Canada. ilie@csd.uwo.ca;Department of Computing and Software, McMaster University, Hamilton ON L8S 4K1, Canada and Digital Ecosystems and Business Intelligence Institute, Curtin University of Technology, Perth WA 6845, A ...
Venue:
Fundamenta Informaticae - Theory that Counts: To Oscar Ibarra on His 70th Birthday
Year:
2011

Citing 16
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Abstract

Unique substrings appear scattered in the stringology literature and have important applications in bioinformatics. In this paper we initiate a study of minimum unique substrings in a given string; that is, substrings that occur exactly once while all their substrings are repeats. We discover a strong duality between minimum unique substrings and maximum repeats which, in particular, allows fast computation of one from the other. We give several optimal algorithms, some of which are very simple and efficient. Their combinatorial properties are investigated and a number of open problems are proposed.