Optimization of Spatial Joins Using Filters

When viewing present-day technical applications that rely on the use of database systems, one notices that new techniques must be integrated in database management systems to be able to support these applications efficiently. This paper discusses one of these techniques in the context of supporting a Geographic Information System. It is known that the use of filters on geometric objects has a significant impact on the processing of 2-way spatial join queries. For this purpose, filters require approximations of objects. Queries can be optimized by filtering data not with just one but with several filters. Existing join methods are based on a combination of filters and a spatial index. The index is used to reduce the cost of the filter step and to minimize the cost of retrieving geometric objects from disk. In this paper we examine n-way spatial joins. Complex n-way spatial join queries require solving several 2-way joins of intermediate results. In this case, not only the profit gained from using both filters and spatial indices but also the additional cost due to using these techniques are examined. For 2-way joins of base relations these costs are considered part of physical database design. We focus on the criteria for mutually comparing filters and not on those for spatial indices. Important aspects of a multi-step filter-based n-way spatial join method are described together with performance experiments. The winning join method uses several filters with approximations that are constructed by rotating two parallel lines around the object

Bounding right-arm rotation distances

Rotation distance measures the difference in shape between binary trees of the same size by counting the minimum number of rotations needed to transform one tree to the other. We describe several types of rotation distance where restrictions are put on the locations where rotations are permitted, and provide upper bounds on distances between trees with a fixed number of nodes with respect to several families of these restrictions. These bounds are sharp in a certain asymptotic sense and are obtained by relating each restricted rotation distance to the word length of elements of Thompson's group F with respect to different generating sets, including both finite and infinite generating sets.Comment: 30 pages, 11 figures. This revised version corrects some typos and has some clearer proofs of the results for the lower bounds and better figure

Area-Universal Rectangular Layouts

A rectangular layout is a partition of a rectangle into a finite set of interior-disjoint rectangles. Rectangular layouts appear in various applications: as rectangular cartograms in cartography, as floorplans in building architecture and VLSI design, and as graph drawings. Often areas are associated with the rectangles of a rectangular layout and it might hence be desirable if one rectangular layout can represent several area assignments. A layout is area-universal if any assignment of areas to rectangles can be realized by a combinatorially equivalent rectangular layout. We identify a simple necessary and sufficient condition for a rectangular layout to be area-universal: a rectangular layout is area-universal if and only if it is one-sided. More generally, given any rectangular layout L and any assignment of areas to its regions, we show that there can be at most one layout (up to horizontal and vertical scaling) which is combinatorially equivalent to L and achieves a given area assignment. We also investigate similar questions for perimeter assignments. The adjacency requirements for the rectangles of a rectangular layout can be specified in various ways, most commonly via the dual graph of the layout. We show how to find an area-universal layout for a given set of adjacency requirements whenever such a layout exists.Comment: 19 pages, 16 figure