{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article10912","name":"Lower Bounds on Non-Adaptive Data Structures Maintaining Sets of Numbers, from Sunflowers","abstract":"We prove new cell-probe lower bounds for dynamic data structures that maintain a subset of {1,2,...,n}, and compute various statistics of the set. The data structure is said to handle insertions non-adaptively if the locations of memory accessed depend only on the element being inserted, and not on the contents of the memory. For any such data structure that can compute the median of the set, we prove that: t_{med} >= Omega(n^{1\/(t_{ins}+1)}\/(w^2 * t_{ins}^2)), where t_{ins} is the number of memory locations accessed during insertions, t_{med} is the number of memory locations accessed to compute the median, and w is the number of bits stored in each memory location. When the data structure is able to perform deletions non-adaptively and compute the minimum non-adaptively, we prove t_{min} + t_{del} >= Omega(log n \/(log w + log log n)), where t_{min} is the number of locations accessed to compute the minimum, and t_{del} is the number of locations accessed to perform deletions. For the predecessor search problem, where the data structure is required to compute the predecessor of any element in the set, we prove that if computing the predecessors can be done non-adaptively, then either t_{pred} >= Omega(log n\/(log log n + log w)), or t_{ins} >= Omega(n^{1\/(2(t_{pred}+1))}), where t_{pred} is the number of locations accessed to compute predecessors.\r\nThese bounds are nearly matched by Binary Search Trees in some range of parameters. Our results follow from using the Sunflower Lemma of Erd\u00f6s and Rado [Paul Erd\u00f6s and Richard Rado, 1960] together with several kinds of encoding arguments.","keywords":["Non-adaptive data structures","Sunflower lemma"],"author":[{"@type":"Person","name":"Natarajan Ramamoorthy, Sivaramakrishnan","givenName":"Sivaramakrishnan","familyName":"Natarajan Ramamoorthy","affiliation":"Paul G. Allen School for Computer Science & Engineering, University of Washington, Seattle, USA","funding":"Supported by the National Science Foundation under agreement CCF-1420268 and CCF-1524251"},{"@type":"Person","name":"Rao, Anup","givenName":"Anup","familyName":"Rao","affiliation":"Paul G. Allen School for Computer Science & Engineering, University of Washington, Seattle, USA","funding":"Supported by the National Science Foundation under agreement CCF-1420268 and CCF-1524251"}],"position":27,"pageStart":"27:1","pageEnd":"27:16","dateCreated":"2018-06-04","datePublished":"2018-06-04","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Natarajan Ramamoorthy, Sivaramakrishnan","givenName":"Sivaramakrishnan","familyName":"Natarajan Ramamoorthy","affiliation":"Paul G. Allen School for Computer Science & Engineering, University of Washington, Seattle, USA","funding":"Supported by the National Science Foundation under agreement CCF-1420268 and CCF-1524251"},{"@type":"Person","name":"Rao, Anup","givenName":"Anup","familyName":"Rao","affiliation":"Paul G. Allen School for Computer Science & Engineering, University of Washington, Seattle, USA","funding":"Supported by the National Science Foundation under agreement CCF-1420268 and CCF-1524251"}],"copyrightYear":"2018","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.CCC.2018.27","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","citation":["http:\/\/dx.doi.org\/10.1145\/256303.256309","http:\/\/dx.doi.org\/10.1016\/j.tcs.2007.02.047"],"isPartOf":{"@type":"PublicationVolume","@id":"#volume6305","volumeNumber":102,"name":"33rd Computational Complexity Conference (CCC 2018)","dateCreated":"2018-06-04","datePublished":"2018-06-04","editor":{"@type":"Person","name":"Servedio, Rocco A.","givenName":"Rocco A.","familyName":"Servedio"},"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article10912","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6305"}}}