Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, July 01, 2004, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Csaba Dávid Tóth (U. of California at Santa Barbara)

Binary space partitions of orthogonal subdivisions

We consider the problem of constructing binary space partitions (BSPs) for orthogonal subdivisions (space filling packings of boxes) in d-space. We show that a subdivision with n boxes can be refined into a BSP of size O(n d+1/3), for all d>2, and that such a partition can be computed in time O(K log n), where K is the size of the BSP produced. Our upper bound on the BSP size is tight for 3-dimensional subdivisions in higher dimensions, this is the first nontrivial result for general full-dimensional boxes. We also present a lower bound construction for a subdivision of n boxes in d-space that requires a BSP of size Ω(nf(d)), where f(d) converges to (1+ √5)/2 as d goes to infinity.

(Joint work with John Hershberger and Subhash Suri)

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