Let A be the incidence matrix of a set system with m sets and n points, m ≤ n, and let t = tr M, where M = AT A. Finally, let σ = tr M2 be the sum of squares of the elements of ...
We propose a simple variant of kd-trees, called rank-based kd-trees, for sets of points in Rd . We show that a rank-based kd-tree, like an ordinary kd-tree, supports range search ...
Mohammad Ali Abam, Mark de Berg, Bettina Speckmann
Let S be a set of n points moving on the real line. The kinetic sorting problem is to maintain a data structure on the set S that makes it possible to quickly generate a sorted li...
We develop a cache-oblivious data structure for storing a set S of N axis-aligned rectangles in the plane, such that all rectangles in S intersecting a query rectangle or point ca...
We introduce a new type of diagram called the VV(c)-diagram (the visibility–Voronoi diagram for clearance c), which is a hybrid between the visibility graph and the Voronoi diag...