{"type":"conference","file_date_updated":"2025-10-27T07:09:41Z","arxiv":1,"acknowledgement":"This work was supported under the Australian Research Council Discovery Projects\r\nfunding scheme (project number DP180102870). This project has received funding from the\r\nEuropean Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 101019564) “The Design of Modern Fully Dynamic Data Structures (MoDynStruct)” and from the Austrian Science Fund (FWF) project Z 422-N and project “Fast Algorithms for a Reactive Network Layer (ReactNet)” P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020–2024.","status":"public","scopus_import":"1","has_accepted_license":"1","_id":"20536","ddc":["000"],"date_created":"2025-10-26T23:01:35Z","quality_controlled":"1","OA_type":"gold","volume":349,"language":[{"iso":"eng"}],"doi":"10.4230/LIPIcs.WADS.2025.47","conference":{"name":"WADS: Algorithms and Data Structures Symposium","location":"Toronto, Canada","end_date":"2025-08-15","start_date":"2025-08-11"},"author":[{"first_name":"Roodabeh","full_name":"Safavi Hemami, Roodabeh","id":"72ed2640-8972-11ed-ae7b-f9c81ec75154","last_name":"Safavi Hemami"},{"full_name":"Seybold, Martin P.","last_name":"Seybold","first_name":"Martin P."}],"corr_author":"1","intvolume":"       349","publication_status":"published","department":[{"_id":"MoHe"}],"oa":1,"day":"29","alternative_title":["LIPIcs"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"external_id":{"arxiv":["2303.04722"]},"article_processing_charge":"No","OA_place":"publisher","title":"B-Treaps revised: Write efficient randomized block search trees with high load","abstract":[{"lang":"eng","text":"Uniquely represented (UR) data structures represent each logical state with a unique storage state. We study the problem of maintaining a dynamic set of n keys from a totally ordered universe in this context. UR structures are also called \"strongly history independent\" structures in the literature.\r\nWe introduce a two-layer data structure called (α,ε)-Randomized Block Search Tree (RBST) that is uniquely represented and suitable for external memory (EM). Though RBSTs naturally generalize the well-known binary Treaps, several new ideas are needed to analyze the expected search, update, and storage efficiency in terms of block-reads, block-writes, and blocks stored. We prove that searches have O(ε^{-1} + log_α n) block-reads, that dynamic updates perform O(ε^{-1} + log_α(n)/α) block-writes and O(ε^{-2}+(1+(ε^{-1}+log n)/α)log_α n) block-reads, and that (α, ε)-RBSTs have an asymptotic load-factor of at least (1-ε) for every ε ∈ (0,1/2].\r\nThus (α, ε)-RBSTs improve on the known, uniquely represented B-Treap [Golovin; ICALP'09]. Compared with non-UR structures, the RBST is also, to the best of our knowledge, the first external memory structure that is storage-efficient and has a non-amortized, write-efficient update bound."}],"file":[{"content_type":"application/pdf","relation":"main_file","checksum":"196af33762831a78e87f4f95ecd8677b","access_level":"open_access","date_created":"2025-10-27T07:09:41Z","date_updated":"2025-10-27T07:09:41Z","success":1,"creator":"dernst","file_id":"20540","file_name":"2025_LIPIcs.WADS_Safavi.pdf","file_size":1081870}],"citation":{"ama":"Safavi Hemami R, Seybold MP. B-Treaps revised: Write efficient randomized block search trees with high load. In: <i>19th International Symposium on Algorithms and Data Structures</i>. Vol 349. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:<a href=\"https://doi.org/10.4230/LIPIcs.WADS.2025.47\">10.4230/LIPIcs.WADS.2025.47</a>","ieee":"R. Safavi Hemami and M. P. Seybold, “B-Treaps revised: Write efficient randomized block search trees with high load,” in <i>19th International Symposium on Algorithms and Data Structures</i>, Toronto, Canada, 2025, vol. 349.","short":"R. Safavi Hemami, M.P. Seybold, in:, 19th International Symposium on Algorithms and Data Structures, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.","ista":"Safavi Hemami R, Seybold MP. 2025. B-Treaps revised: Write efficient randomized block search trees with high load. 19th International Symposium on Algorithms and Data Structures. WADS: Algorithms and Data Structures Symposium, LIPIcs, vol. 349, 47.","apa":"Safavi Hemami, R., &#38; Seybold, M. P. (2025). B-Treaps revised: Write efficient randomized block search trees with high load. In <i>19th International Symposium on Algorithms and Data Structures</i> (Vol. 349). Toronto, Canada: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.WADS.2025.47\">https://doi.org/10.4230/LIPIcs.WADS.2025.47</a>","chicago":"Safavi Hemami, Roodabeh, and Martin P. Seybold. “B-Treaps Revised: Write Efficient Randomized Block Search Trees with High Load.” In <i>19th International Symposium on Algorithms and Data Structures</i>, Vol. 349. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. <a href=\"https://doi.org/10.4230/LIPIcs.WADS.2025.47\">https://doi.org/10.4230/LIPIcs.WADS.2025.47</a>.","mla":"Safavi Hemami, Roodabeh, and Martin P. Seybold. “B-Treaps Revised: Write Efficient Randomized Block Search Trees with High Load.” <i>19th International Symposium on Algorithms and Data Structures</i>, vol. 349, 47, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025, doi:<a href=\"https://doi.org/10.4230/LIPIcs.WADS.2025.47\">10.4230/LIPIcs.WADS.2025.47</a>."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","year":"2025","project":[{"name":"The design and evaluation of modern fully dynamic data structures","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","grant_number":"101019564","call_identifier":"H2020"},{"grant_number":"Z00422","name":"Efficient algorithms","_id":"34def286-11ca-11ed-8bc3-da5948e1613c"},{"grant_number":"P33775","_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","name":"Fast Algorithms for a Reactive Network Layer"}],"article_number":"47","publication_identifier":{"isbn":["9783959773980"],"issn":["1868-8969"]},"month":"08","ec_funded":1,"date_updated":"2025-10-27T07:10:49Z","oa_version":"Published Version","publication":"19th International Symposium on Algorithms and Data Structures","date_published":"2025-08-29T00:00:00Z"}