Separating sets of hyperrectangles

Part of the Lecture Notes in Computer Science book series (LNCS, volume 452)


We consider the problem of separating a given set of d-dimensional non-overlapping isothetic hyperrectangles by means of one cutting isothetic hyperplane. If the cutting hyperplane crosses one hyperrectangle this is split into two non-overlapping hyperrectangles. We show that there always exists a cutting hyperplane which separates n given hyperrectangles into two sets each containing no more than ⌈nd⌊ hyperrectangles, where αd=2d/(2d−1). Also, we show that it is not possible to do better. Moreover, we provide an O(d·n) time algorithm for finding this cutting hyperplane.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  1. 1.Department of Computer and System ScienceUniversity of Roma “La Sapienza”RomaItaly
  2. 2.Consiglio Nazionale delle RicercheIstituto di Analisi dei Sistemi ed InformaticaRomaItaly

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