{"file":[{"creator":"dernst","file_name":"2023_LIPICS_HenzingerM.pdf","success":1,"relation":"main_file","checksum":"22141ab8bc55188e2dfff665e5daecbd","access_level":"open_access","date_created":"2023-03-27T06:37:22Z","date_updated":"2023-03-27T06:37:22Z","file_size":872706,"file_id":"12769","content_type":"application/pdf"}],"ddc":["000"],"title":"Dynamic maintenance of monotone dynamic programs and applications","article_number":"36","conference":{"start_date":"2023-03-07","name":"STACS: Symposium on Theoretical Aspects of Computer Science","location":"Hamburg, Germany","end_date":"2023-03-09"},"date_created":"2023-03-26T22:01:07Z","has_accepted_license":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","month":"03","publication_status":"published","language":[{"iso":"eng"}],"quality_controlled":"1","acknowledgement":"Monika Henzinger: This project has received funding from the European Research Council\r\n(ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant\r\nagreement No. 101019564 “The Design of Modern Fully Dynamic Data Structures (MoDynStruct)” and from the Austrian Science Fund (FWF) project “Fast Algorithms for a Reactive Network Layer (ReactNet)”, P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020–2024.\r\nStefan Neumann: This research is supported by the the ERC Advanced Grant REBOUND (834862) and the EC H2020 RIA project SoBigData++ (871042).\r\nStefan Schmid: Research supported by Austrian Science Fund (FWF) project I 5025-N (DELTA), 2020-2024.","citation":{"short":"M.H. Henzinger, S. Neumann, H. Räcke, S. Schmid, in:, 40th International Symposium on Theoretical Aspects of Computer Science, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023.","ama":"Henzinger MH, Neumann S, Räcke H, Schmid S. Dynamic maintenance of monotone dynamic programs and applications. In: <i>40th International Symposium on Theoretical Aspects of Computer Science</i>. Vol 254. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:<a href=\"https://doi.org/10.4230/LIPIcs.STACS.2023.36\">10.4230/LIPIcs.STACS.2023.36</a>","mla":"Henzinger, Monika H., et al. “Dynamic Maintenance of Monotone Dynamic Programs and Applications.” <i>40th International Symposium on Theoretical Aspects of Computer Science</i>, vol. 254, 36, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023, doi:<a href=\"https://doi.org/10.4230/LIPIcs.STACS.2023.36\">10.4230/LIPIcs.STACS.2023.36</a>.","ieee":"M. H. Henzinger, S. Neumann, H. Räcke, and S. Schmid, “Dynamic maintenance of monotone dynamic programs and applications,” in <i>40th International Symposium on Theoretical Aspects of Computer Science</i>, Hamburg, Germany, 2023, vol. 254.","apa":"Henzinger, M. H., Neumann, S., Räcke, H., &#38; Schmid, S. (2023). Dynamic maintenance of monotone dynamic programs and applications. In <i>40th International Symposium on Theoretical Aspects of Computer Science</i> (Vol. 254). Hamburg, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.STACS.2023.36\">https://doi.org/10.4230/LIPIcs.STACS.2023.36</a>","chicago":"Henzinger, Monika H, Stefan Neumann, Harald Räcke, and Stefan Schmid. “Dynamic Maintenance of Monotone Dynamic Programs and Applications.” In <i>40th International Symposium on Theoretical Aspects of Computer Science</i>, Vol. 254. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. <a href=\"https://doi.org/10.4230/LIPIcs.STACS.2023.36\">https://doi.org/10.4230/LIPIcs.STACS.2023.36</a>.","ista":"Henzinger MH, Neumann S, Räcke H, Schmid S. 2023. Dynamic maintenance of monotone dynamic programs and applications. 40th International Symposium on Theoretical Aspects of Computer Science. STACS: Symposium on Theoretical Aspects of Computer Science, LIPIcs, vol. 254, 36."},"file_date_updated":"2023-03-27T06:37:22Z","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)"},"year":"2023","department":[{"_id":"MoHe"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.4230/LIPIcs.STACS.2023.36","date_updated":"2023-03-27T06:46:27Z","publication_identifier":{"issn":["1868-8969"],"isbn":["9783959772662"]},"date_published":"2023-03-01T00:00:00Z","abstract":[{"lang":"eng","text":"Dynamic programming (DP) is one of the fundamental paradigms in algorithm design. However,\r\nmany DP algorithms have to fill in large DP tables, represented by two-dimensional arrays, which causes at least quadratic running times and space usages. This has led to the development of improved algorithms for special cases when the DPs satisfy additional properties like, e.g., the Monge property or total monotonicity.\r\nIn this paper, we consider a new condition which assumes (among some other technical assumptions) that the rows of the DP table are monotone. Under this assumption, we introduce\r\na novel data structure for computing (1 + ϵ)-approximate DP solutions in near-linear time and\r\nspace in the static setting, and with polylogarithmic update times when the DP entries change\r\ndynamically. To the best of our knowledge, our new condition is incomparable to previous conditions and is the first which allows to derive dynamic algorithms based on existing DPs. Instead of using two-dimensional arrays to store the DP tables, we store the rows of the DP tables using monotone piecewise constant functions. This allows us to store length-n DP table rows with entries in [0, W] using only polylog(n, W) bits, and to perform operations, such as (min, +)-convolution or rounding, on these functions in polylogarithmic time.\r\nWe further present several applications of our data structure. For bicriteria versions of k-balanced graph partitioning and simultaneous source location, we obtain the first dynamic algorithms with subpolynomial update times, as well as the first static algorithms using only near-linear time and space. Additionally, we obtain the currently fastest algorithm for fully dynamic knapsack."}],"intvolume":"       254","author":[{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","first_name":"Monika H","full_name":"Henzinger, Monika H","last_name":"Henzinger"},{"first_name":"Stefan","full_name":"Neumann, Stefan","last_name":"Neumann"},{"full_name":"Räcke, Harald","first_name":"Harald","last_name":"Räcke"},{"first_name":"Stefan","full_name":"Schmid, Stefan","last_name":"Schmid"}],"article_processing_charge":"No","oa":1,"oa_version":"Published Version","day":"01","scopus_import":"1","type":"conference","alternative_title":["LIPIcs"],"_id":"12760","external_id":{"arxiv":["2301.01744"]},"publication":"40th International Symposium on Theoretical Aspects of Computer Science","status":"public","volume":254}