[{"language":[{"iso":"eng"}],"project":[{"_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","grant_number":"101019564","name":"The design and evaluation of modern fully dynamic data structures","call_identifier":"H2020"}],"article_processing_charge":"Yes","oa":1,"article_number":"101","department":[{"_id":"MoHe"}],"scopus_import":"1","ddc":["000"],"volume":388,"quality_controlled":"1","doi":"10.4230/LIPIcs.ESA.2026.101","acknowledgement":"Ivor van der Hoog, Eva Rotenberg, and Daniel Rutschmann thank the VILLUM Foundation\r\ngrant (VIL37507) “Efficient Recomputations for Changeful Problems” for supporting this work.\r\nDaniel Rutschmann is supported by the European Research Council (ERC) under the European\r\nUnion’s Horizon 2020 research and innovation programme (No. 101019564) ","alternative_title":["LIPIcs"],"_id":"22915","date_published":"2026-08-25T00:00:00Z","status":"public","year":"2026","ec_funded":1,"publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_identifier":{"isbn":["9783959774451"],"issn":["1868-8969"]},"citation":{"ama":"Van Der Hoog I, Rotenberg E, Rutschmann DP. Tight Better-Than-Worst-Case bounds for element distinctness and set intersection. In: <i>34th Annual European Symposium on Algorithms</i>. Vol 388. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:<a href=\"https://doi.org/10.4230/LIPIcs.ESA.2026.101\">10.4230/LIPIcs.ESA.2026.101</a>","apa":"Van Der Hoog, I., Rotenberg, E., &#38; Rutschmann, D. P. (2026). Tight Better-Than-Worst-Case bounds for element distinctness and set intersection. In <i>34th Annual European Symposium on Algorithms</i> (Vol. 388). L’Aquila, Italy: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.ESA.2026.101\">https://doi.org/10.4230/LIPIcs.ESA.2026.101</a>","ieee":"I. Van Der Hoog, E. Rotenberg, and D. P. Rutschmann, “Tight Better-Than-Worst-Case bounds for element distinctness and set intersection,” in <i>34th Annual European Symposium on Algorithms</i>, L’Aquila, Italy, 2026, vol. 388.","mla":"Van Der Hoog, Ivor, et al. “Tight Better-Than-Worst-Case Bounds for Element Distinctness and Set Intersection.” <i>34th Annual European Symposium on Algorithms</i>, vol. 388, 101, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:<a href=\"https://doi.org/10.4230/LIPIcs.ESA.2026.101\">10.4230/LIPIcs.ESA.2026.101</a>.","chicago":"Van Der Hoog, Ivor, Eva Rotenberg, and Daniel P Rutschmann. “Tight Better-Than-Worst-Case Bounds for Element Distinctness and Set Intersection.” In <i>34th Annual European Symposium on Algorithms</i>, Vol. 388. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. <a href=\"https://doi.org/10.4230/LIPIcs.ESA.2026.101\">https://doi.org/10.4230/LIPIcs.ESA.2026.101</a>.","short":"I. Van Der Hoog, E. Rotenberg, D.P. Rutschmann, in:, 34th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026.","ista":"Van Der Hoog I, Rotenberg E, Rutschmann DP. 2026. Tight Better-Than-Worst-Case bounds for element distinctness and set intersection. 34th Annual European Symposium on Algorithms. ESA: European Symposium on Algorithms, LIPIcs, vol. 388, 101."},"conference":{"start_date":"2026-08-31","name":"ESA: European Symposium on Algorithms","location":"L’Aquila, Italy","end_date":"2026-09-04"},"intvolume":"       388","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa_version":"Published Version","abstract":[{"text":"The element distinctness problem takes as input a list I of n values from a totally ordered universe, where pairwise comparisons between values are allowed, and the goal is to decide whether I contains any duplicates. It is a well-studied problem with a classical worst-case Ω(n log n) comparison-based lower bound by Fredman [TCS'76]. At first glance, this lower bound appears to rule out any algorithm more efficient than the naive approach of sorting I and comparing adjacent elements. However, upon closer inspection, the Ω(n log n) bound is overly pessimistic. For instance, if I contains n/2 identical elements, a median-finding algorithm will, regardless of the input order, find a duplicate in linear time. This raises a natural question: Are there comparison-based lower bounds for element distinctness that are sensitive to the amount of duplicates in the input instance?\r\nTo address this question, we derive instance-specific lower bounds. For any input instance I, we represent the combinatorial structure of the duplicates in I by an undirected graph G(I) that connects identical elements. Each such graph G is a union of cliques, and we study algorithms by their worst-case running time over all inputs I' with G(I') ≅ G. We establish an adversarial lower bound showing that, for any deterministic algorithm 𝒜, there exists a graph G and an algorithm 𝒜' that, for all inputs I with G(I) ≅ G, is a factor O(log log n) faster than 𝒜. Consequently, no deterministic algorithm can be o(log log n)-competitive for all graphs G. We complement this with an O(log log n)-competitive deterministic algorithm, thereby obtaining tight bounds for element distinctness that go beyond classical worst-case analysis. Subsequently, we study the related problem of set intersection. We show that no deterministic set intersection algorithm can be o(log n)-competitive, and provide an O(log n)-competitive deterministic algorithm. We find it interesting and surprising to discover tight O(log log n)-competitive bounds for element distinctness. Moreover, we find the separation between element distinctness and the set intersection problem unexpected.","lang":"eng"}],"corr_author":"1","file":[{"date_updated":"2026-09-16T09:20:49Z","file_size":892322,"file_name":"2026_LIPIcsESA_vanderHoog.pdf","access_level":"open_access","relation":"main_file","success":1,"creator":"dernst","content_type":"application/pdf","checksum":"c552853bfa37e4b9a0f060107e464ed0","file_id":"22937","date_created":"2026-09-16T09:20:49Z"}],"keyword":["Comparison-based analysis","set intersection","universal optimality"],"external_id":{"arxiv":["2511.02954"]},"OA_type":"gold","das_tickbox":"0","type":"conference","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"25","author":[{"full_name":"Van Der Hoog, Ivor","first_name":"Ivor","last_name":"Van Der Hoog"},{"full_name":"Rotenberg, Eva","last_name":"Rotenberg","first_name":"Eva"},{"id":"7397d908-b582-11f0-bf73-88b902e86527","full_name":"Rutschmann, Daniel P","first_name":"Daniel P","last_name":"Rutschmann"}],"arxiv":1,"license":"https://creativecommons.org/licenses/by/4.0/","month":"08","date_updated":"2026-09-16T09:21:35Z","fulldoi":"https://doi.org/10.4230/LIPIcs.ESA.2026.101","supplementarymaterial":"yes","researchdata_availability":"no","file_date_updated":"2026-09-16T09:20:49Z","date_created":"2026-09-13T22:01:52Z","publication":"34th Annual European Symposium on Algorithms","OA_place":"publisher","title":"Tight Better-Than-Worst-Case bounds for element distinctness and set intersection","has_accepted_license":"1"}]