2026-09-22T03:10:15Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:26049 2026-09-05T19:35:53Z ddc:004 open_access

Faster Algorithms for Shortest Unique or Absent Substrings Charalampopoulos, Panagiotis Mohamed, Manal Pissis, Solon P. Verbeek, Hilde Zuba, Wiktor string algorithms unique substrings absent substrings absent words We revisit two well-known algorithmic problems on strings: computing a shortest unique substring (SUS) and a shortest absent substring (SAS) in a string S of length n. Both problems admit folklore 𝒪(n)-time solutions using the suffix tree of S. However, for small alphabets, this complexity is not necessarily optimal in the word RAM model, where a string of length n over alphabet [0,σ) can be stored in 𝒪(n log σ/log n) space and read in 𝒪(n log σ/log n) time. We present an 𝒪(n log σ/√{log n})-time algorithm for computing a SUS in S. This algorithm decomposes the problem according to the length and the period of the sought substring and uses several tools and techniques, such as synchronizing sets, the analysis of runs, and wavelet trees, to reduce the computation of a SUS to a simple geometric problem. Further, we adapt this algorithm and combine it with an efficient construction of de Bruijn sequences in order to obtain an 𝒪(n log σ/√{log n})-time algorithm for computing a SAS in S. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Panagiotis Charalampopoulos and Manal Mohamed and Solon P. Pissis and Hilde Verbeek and Wiktor Zuba 2026 Is Part Of LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SWAT.2026.13 urn:nbn:de:0030-drops-260493 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.13 eng https://creativecommons.org/licenses/by/4.0/legalcode