{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T04:33:01Z","timestamp":1791174781423,"version":"4.1.0"},"reference-count":8,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p>\n                    Dynamic storage allocation is the problem of packing given axis-aligned rectangles into a horizontal strip of minimum height by sliding the rectangles vertically but not horizontally. Where L= is the maximum sum of heights of rectangles that intersect any vertical line and OPT is the minimum height of the enclosing strip, it is obvious that $\\ensuremath{\\text{\\it OPT}}\\ge \\ensuremath{\\text{\\it LOAD}}$; previous work showed that $\\ensuremath{\\text{\\it OPT}}\\le 3\\cdot LOAD. We continue the study of the relationship between OPT and LOAD, proving that OPT=L+O((h\n                    <jats:sub>max<\/jats:sub>\n                    \/L)\n                    <jats:sup>1\/7<\/jats:sup>\n                    )L, where h\n                    <jats:sub>max<\/jats:sub>\n                    is the maximum job height. Conversely, we prove that for any $\\epsilon &gt; 0$, there exists a c&gt;0 such that for all sufficiently large integers $h_{\\max}$, there is a dynamic storage allocation instance with maximum job height $h_{\\max}$, maximum load at most L, and $\\ensuremath{\\text{\\it OPT}}\\geq L+c(h_{\\max}\/L)^{1\/2+\\epsilon}L$, for infinitely many integers L. En route, we construct several new polynomial-time approximation algorithms for dynamic storage allocation, including a $(2+\\epsilon)$-approximation algorithm for the general case and polynomial-time approximation schemes for several natural special cases.\n                  <\/jats:p>","DOI":"10.1137\/s0097539703423941","type":"journal-article","created":{"date-parts":[[2004,4,1]],"date-time":"2004-04-01T21:00:51Z","timestamp":1080853251000},"page":"632-646","source":"Crossref","is-referenced-by-count":32,"title":["<i>OPT<\/i>\n                    Versus\n                    <i>LOAD<\/i>\n                    in Dynamic Storage Allocation"],"prefix":"10.1137","volume":"33","author":[{"given":"Adam L.","family":"Buchsbaum","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Howard","family":"Karloff","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Claire","family":"Kenyon","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nick","family":"Reingold","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mikkel","family":"Thorup","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,2,17]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1051\/ita\/1988220404871"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04245-8"},{"key":"R3","volume-title":"Computers and intractability","author":"Garey Michael","year":"1979"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"Jordan Gergov, Approximation algorithms for dynamic storage allocation, Lecture Notes in Comput. Sci., Vol. 1136, Springer, Berlin, 1996, 52\u2013611469226","DOI":"10.1007\/3-540-61680-2_46"},{"key":"R5","unstructured":", Proceedings of the Tenth Annual ACM\u2010SIAM Symposium on Discrete Algorithms, Association for Computing Machinery (ACM), 1999, 0\u20130, xviii+992, Held in Baltimore, MD, January 17\u201319, 19992000j:68006"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/0401048"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(91)90011-P"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511662072"}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0097539703423941","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:17:31Z","timestamp":1787336251000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0097539703423941"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":8,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1137\/S0097539703423941"],"URL":"https:\/\/doi.org\/10.1137\/s0097539703423941","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,1]]}}}