{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T08:07:06Z","timestamp":1787386026632,"version":"build-2736575974"},"reference-count":31,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[2000,1]]},"abstract":"<jats:p>We consider the practical problem of constructing binary space partitions (BSPs) for a set S of n orthogonal, nonintersecting, two-dimensional rectangles in ${\\Bbb R}^3$ such that the aspect ratio of each rectangle in S is at most $\\alpha$, for some constant $\\alpha \\geq 1$. We present an $n2^{O(\\sqrt{\\log n})}$-time algorithm to build a binary space partition of size $n2^{O(\\sqrt{\\log n})}$ for S. We also show that if m of the n rectangles in S have aspect ratios greater than $\\alpha$, we can construct a BSP of size $n\\sqrt{m}2^{O(\\sqrt{\\log n})}$ for S in $n\\sqrt{m}2^{O(\\sqrt{\\log n})}$ time. The constants of proportionality in the big-oh terms are linear in $\\log \\alpha$. We extend these results to cases in which the input contains nonorthogonal or intersecting objects.<\/jats:p>","DOI":"10.1137\/s0097539797320578","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1422-1448","source":"Crossref","is-referenced-by-count":21,"title":["Binary Space Partitions for Fat Rectangles"],"prefix":"10.1137","volume":"29","author":[{"given":"Pankaj K.","family":"Agarwal","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Edward F.","family":"Grove","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T. M.","family":"Murali","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jeffrey Scott","family":"Vitter","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,27]]},"reference":[{"key":"R1","unstructured":"Pankaj Agarwal, Jeff Erickson, Leonidas Guibas, Kinetic binary space partitions for intersecting segments and disjoint triangles (extended abstract), ACM, New York, 1998, 107\u20131161642918"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"P. K. Agarwal, L. J. Guibas, T. M. Murali, and J. S. Vitter,\n                      Cylindrical static and kinetic binary space partitions\n                      , in Proceedings of the 13th ACM Symposium on Comput. 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