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Kinetic kd-Trees and Longest-Side kd-Trees Abam, Mohammad de Berg, Mark Speckmann, Bettina Kinetic data structures kd-tree longest-side kd-tree We propose a simple variant of kd-trees, called rank-based kd-trees, for sets of points in~$Reals^d$. We show that a rank-based kd-tree, like an ordinary kd-tree, supports range search que-ries in~$O(n^{1-1/d}+k)$ time, where~$k$ is the output size. The main advantage of rank-based kd-trees is that they can be efficiently kinetized: the KDS processes~$O(n^2)$ events in the worst case, assuming that the points follow constant-degree algebraic trajectories, each event can be handled in~$O(log n)$ time, and each point is involved in~$O(1)$ certificates. We also propose a variant of longest-side kd-trees, called rank-based longest-side kd-trees (RBLS kd-trees, for short), for sets of points in~$Reals^2$. RBLS kd-trees can be kinetized efficiently as well and like longest-side kd-trees, RBLS kd-trees support nearest-neighbor, farthest-neighbor, and approximate range search queries in~$O((1/epsilon)log^2 n)$ time. The KDS processes~$O(n^3log n)$ events in the worst case, assuming that the points follow constant-degree algebraic trajectories; each event can be handled in~$O(log^2 n)$ time, and each point is involved in~$O(log n)$ certificates. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Mohammad Abam and Mark de Berg and Bettina Speckmann 2008 Is Part Of Dagstuhl Seminar Proceedings, Volume 8081, Data Structures (2008) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.08081.2 urn:nbn:de:0030-drops-15307 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08081.2 eng https://creativecommons.org/licenses/by/4.0/legalcode