2026-07-23T16:05:08Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:13955 2024-03-06T10:52:59Z ddc:004 open_access

Ranking Bracelets in Polynomial Time Adamson, Duncan Gusev, Vladimir V. Potapov, Igor Deligkas, Argyrios Bracelets Ranking Necklaces The main result of the paper is the first polynomial-time algorithm for ranking bracelets. The time-complexity of the algorithm is O(k²⋅ n⁴), where k is the size of the alphabet and n is the length of the considered bracelets. The key part of the algorithm is to compute the rank of any word with respect to the set of bracelets by finding three other ranks: the rank over all necklaces, the rank over palindromic necklaces, and the rank over enclosing apalindromic necklaces. The last two concepts are introduced in this paper. These ranks are key components to our algorithm in order to decompose the problem into parts. Additionally, this ranking procedure is used to build a polynomial-time unranking algorithm. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Duncan Adamson and Vladimir V. Gusev and Igor Potapov and Argyrios Deligkas 2021 Is Part Of LIPIcs, Volume 191, 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CPM.2021.4 urn:nbn:de:0030-drops-139554 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2021.4 eng https://creativecommons.org/licenses/by/4.0/legalcode