A technique for adding range restrictions to generalized searching problems

In a generalized searching problem, a set $S$ of $n$ colored geometric objects has to be stored in a data structure, such that for any given query object $q$, the distinct colors of the objects of $S$ intersected by $q$ can be reported efficiently. In this paper, a general technique is presented for adding a range restriction to such a problem. The technique is applied to the problem of querying a set of colored points (resp.\ fat triangles) with a fat triangle (resp.\ point). For both problems, a data structure is obtained having size $O(n^{1+\epsilon})$ and query time $O((\log n)^2 + C)$. Here, $C$ denotes the number of colors reported by the query, and $\epsilon$ is an arbitrarily small positive constant

A Technique for Adding Range Restrictions to Generalized Searching Problems

In a generalized searching problem, a set S of n colored geometric objects has to be stored in a data structure, such that for any given query object q, the distinct colors of the objects of S intersected by q can be reported efficiently. In this paper, a general technique is presented for adding a range restriction to such a problem. The technique is applied to the problem of querying a set of colored points (resp. fat triangles) with a fat triangle (resp. point). For both problems, a data structure is obtained having size O(n 1+ffl ) and query time O((log n) 2 + C). Here, C denotes the number of colors reported by the query, and ffl is an arbitrarily small positive constant. Keywords: Computational geometry, data structures, intersection searching, range restriction. 1 Introduction Geometric searching problems arise in a large variety of application areas, such as computer graphics, robotics, VLSI layout design, and databases. In such a problem, a set S of n geometric objects h..