{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:59Z","timestamp":1753893839604,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $S$ be a set of $n$ points in the plane, and let $\\mathcal{D}$ be an arbitrary set of disks, each having a pair of points of $S$ as a diameter. We show that the combinatorial complexity of the union of $\\mathcal{D}$ is $O(n^{3\/2})$, and provide a lower bound construction with $\\Omega(n^{4\/3})$ complexity. If the points of $S$ are in convex position, the upper bound drops to $O(n\\log n)$.<\/jats:p>","DOI":"10.37236\/2681","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:32:06Z","timestamp":1578706326000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Union Complexity of Diametral Disks"],"prefix":"10.37236","volume":"20","author":[{"given":"Boris","family":"Aronov","sequence":"first","affiliation":[]},{"given":"Muriel","family":"Dulieu","sequence":"additional","affiliation":[]},{"given":"Rom","family":"Pinchasi","sequence":"additional","affiliation":[]},{"given":"Micha","family":"Sharir","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,6,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i2p53\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i2p53\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:19:03Z","timestamp":1579259943000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i2p53"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6,7]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2013,4,9]]}},"URL":"https:\/\/doi.org\/10.37236\/2681","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,6,7]]},"article-number":"P53"}}