Segment Intersection Searching Problems in General Settings

Algorithms for Some Intersection Searching Problems Involving Curved Objects

Two classes of geometric intersection searching problems are considered i e problems in which a set S of geometric objects is to be preprocessed into a data structure so that for any query object q the objects of S that are intersected by q can be counted or reported e ciently In the rst class S is a set of curved objects such as d balls d spheres circles or circular arcs and q is also a curved...

Algorithms for Generalized Halfspace Range Searching and Other Intersection Searching Problems

In a generalized intersection searching problem, a set S of colored geometric objects is to be preprocessed so that, given a query object q, the distinct colors of the objects of S that are intersected by q can be reported or counted efficiently. These problems generalize the well-studied standard intersection searching problems and have many applications. Unfortunately, the solutions known for...

Geometric Intersection Graphs: Problems and Directions Collection of Open Problems 1. Coloring segment intersection graphs avoiding monochromatic cliques Proposer:

For a graph G and an integer k ≥ 2, let χk(G) denote the minimum number of colors in a coloring of the vertices of G such that no k-clique of G is monochromatic. In particular, χ2(G) is the ordinary chromatic number of G. It is known that triangle-free segment intersection graphs can have arbitrarily large chromatic number. It is also known that Kk-free string graphs can have arbitrarily large ...

Computational geometry: Generalized intersection searching

A General Technique for Top-$k$ Geometric Intersection Query Problems

In a top-k Geometric Intersection Query (top-k GIQ) problem, a set of n weighted, geometric objects in Rd is to be pre-processed into a compact data structure so that for any query geometric object, q, and integer k > 0, the k largest-weight objects intersected by q can be reported efficiently. While the top-k problem has been studied extensively for non-geometric problems (e.g., recommender sy...