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Algorithms"],"published-print":{"date-parts":[[2024,10,31]]},"abstract":"<jats:p>\n            <jats:italic>Data-structure dynamization<\/jats:italic>\n            is a general approach for making static data structures dynamic. It is used extensively in geometric settings and in the guise of so-called\n            <jats:italic>merge (or compaction)<\/jats:italic>\n            policies in big-data databases such as LevelDB and Google Bigtable. Previous theoretical work is based on worst-case analyses for uniform inputs\u2014insertions of one item at a time and non-varying read rate. In practice, merge policies must not only handle batch insertions and varying read\/write ratios, they can take advantage of such non-uniformity to reduce cost on a per-input basis. To model this, we initiate the study of data-structure dynamization through the lens of competitive analysis via two new online set-cover problems. For each, the input is a sequence of disjoint sets of weighted items. The sets are revealed one at a time. The algorithm must respond to each with a set cover that covers all items revealed so far. It obtains the cover incrementally from the previous cover by adding one or more sets and optionally removing existing sets. For each new set the algorithm incurs\n            <jats:italic>build cost<\/jats:italic>\n            equal to the weight of the items in the set. In the first problem the objective is to minimize total build cost plus total\n            <jats:italic>query cost<\/jats:italic>\n            , where the algorithm incurs a query cost at each time\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(t\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            equal to the current cover size. In the second problem, the objective is to minimize the build cost while keeping the query cost from exceeding\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(k\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            (a given parameter) at any time. We give deterministic online algorithms for both variants, with competitive ratios of\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(\\Theta(\\log^{*}n)\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            and\n            <jats:inline-formula content-type=\"math\/tex\">\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(k\\)<\/jats:tex-math>\n            <\/jats:inline-formula>\n            , respectively. The latter ratio is optimal for the second variant.\n          <\/jats:p>","DOI":"10.1145\/3672614","type":"journal-article","created":{"date-parts":[[2024,6,28]],"date-time":"2024-06-28T13:46:45Z","timestamp":1719582405000},"page":"1-28","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Competitive Data-Structure Dynamization"],"prefix":"10.1145","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0517-112X","authenticated-orcid":false,"given":"Claire","family":"Mathieu","sequence":"first","affiliation":[{"name":"CNRS, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-3610-9918","authenticated-orcid":false,"given":"Rajmohan","family":"Rajaraman","sequence":"additional","affiliation":[{"name":"Northeastern University, Boston, MA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8144-3345","authenticated-orcid":false,"given":"Neal E.","family":"Young","sequence":"additional","affiliation":[{"name":"University of California Riverside, Riverside, CA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8760-539X","authenticated-orcid":false,"given":"Arman","family":"Yousefi","sequence":"additional","affiliation":[{"name":"Google, Los Angeles, CA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2024,10,11]]},"reference":[{"key":"e_1_3_4_2_2","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/3-540-48224-5_10","volume-title":"Automata, Languages and Programming (Lecture Notes in Computer Science)","author":"Agarwal Pankaj K.","year":"2001","unstructured":"Pankaj K. 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