We develop external data structures for storing points in one or two dimensions, each moving along a linear trajectory, so that a range query at a given time tq can be answered efficiently. The novel feature of our data structures is that the number of I/Os required to answer a query depends not only on the size of the data set and on the number of points in the answer but also on the differenc...

In this paper, we formulate two classes of problems, the colored range query problems and the colored point enclosure query problems to model multi-dimensional range and point enclosure queries in the presence of categorical information. Many of these problems are difficult to solve using traditional data structural techniques. Based on a new framework of combining sketching techniques and trad...

We consider the problem of reporting convex hull points in an orthogonal range query in two dimensions. Formally, let P be a set of n points in R. A point lies on the convex hull of a point set S if it lies on the boundary of the minimum convex polygon formed by S. In this paper, we are interested in finding the points that lie on the boundary of the convex hull of the points in P that also fal...

We give efficient algorithms and index data structures for range search in general metric spaces. We give a simple methods to make almost any existing algorithm memory adaptive, improving the search the more memory is available. For vector spaces and metric space of strings we show how several distances can be computed in bit-parallelly, in sequential computer, and use the result to improve the...

We consider the planar convex hull range query problem. Let P be a set of points in the plane. We preprocess these points into a data structure such that given an orthogonal range query, we can report the convex hull of the points in the range in O(log n + h) time, where h is the size of the output. The data structure uses O(n log n) space. This improves the previous bound of O(log n+h) time an...

In this paper we study the node distribution of an Rtree storing region data, like for instance islands, lakes or human-inhabited areas. We will show that real region datasets are packed in minimum bounding rectangles (MBRs) whose area distribution follows the same power law, named REGAL (REGion Area Law) [12], as that for the regions themselves. Moreover, these MBRs are packed in their turn in...

We consider indexing and range searching in metric spaces. The best method known is AESA, in practice requiring the fewest number of distance evaluations to answer range queries. The problem with AESA is its space complexity, requiring storage for Θ(n) distance values to index n objects. We give several methods to reduce this cost. The main observation is that exact distance values are not need...

We present a practical implementation of the first adaptive data structure for orthogonal range queries in 2D [Arroyuelo et al., ISAAC 2009]. The structure is static, requires only linear space for its representation, and can even be made implicit. The running time for a query is O(k lg n+m), where k is the number of non-crossing monotonic chains in which we can partition the set of points, and...

There has been a renewal of interest in data structures for range extremum queries. In such problems, the input comprises N points, which are either elements of a d-dimensional matrix, that is, their coordinates are specified by the 1D submatrices they lie in (row and column indices for d = 2), or they are points in IR. Furthermore, associated with each point is a priority that is independent o...

Range searching, a fundamental problem in numerous applications areas, has been widely studied in computational geometry and spatial databases. Given a set of geometric objects, a typical range query asks for reporting all the objects that intersect a query object. However in many applications, including databases and network routing, input objects are partitioned into categories and a query as...