{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:00Z","timestamp":1753893840251,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $\\mathcal{R}$ be a family of $n$ axis-parallel rectangles with packing number $p-1$, meaning that among any $p$ of the rectangles, there are two with a non-empty intersection. We show that the union complexity of $\\mathcal{R}$ is at most $O(n+p^2)$, and that the $(k-1)$-level complexity of $\\mathcal{R}$ is at most $O(n+k p^2)$. Both upper bounds are tight.<\/jats:p>","DOI":"10.37236\/6792","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:02:41Z","timestamp":1578650561000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Union Complexity of Families of Axis-Parallel Rectangles with a Low Packing Number"],"prefix":"10.37236","volume":"25","author":[{"given":"Chaya","family":"Keller","sequence":"first","affiliation":[]},{"given":"Shakhar","family":"Smorodinsky","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,11,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p32\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p32\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:21:37Z","timestamp":1579216897000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i4p32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,16]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,10,5]]}},"URL":"https:\/\/doi.org\/10.37236\/6792","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,11,16]]},"article-number":"P4.32"}}