Identifying and quantifying the size of multiple intersections among a large number of axis-aligned geometric objects is an essential computational geometry problem. The ability to solve this problem can effectively inform a number of spatial data mining methods and can provide support in decision making for a variety of applications. Currently, the state-of-the-art approach for addressing such intersection problems resorts to an algorithmic paradigm, collectively known as the sweep-line algorithm. However, its application on specific instances of the problem inherits a number of limitations. With that mind, we design and implement a novel, exact, fast and scalable yet versatile, sweep-line based algorithm, named SLIG. Our algorithm can be employed in a number of problems and applications involving the efficient computation of numerous axis-aligned object intersection problems in multiple dimensions. The key idea of our algorithm lies in constructing an auxiliary data structure when the sweep line algorithm is applied, an intersection graph. This graph can effectively be used to provide connectivity properties among overlapping objects, as well as to inform the much harder problem of finding the location and size of the common area defined by multiple overlapping objects. A thorough experimental evaluation on synthetic data of various characteristics and sizes, demonstrates that SLIG performs significantly faster than classic sweep-line based algorithms. SLIG is not only faster and more versatile, but also provides a suite of powerful querying capabilities. To support the reproducibility of our methods, we make source code and datasets available.

The MIX mediator system, MIXm, is developed as part of the MIX Project at the San Diego Supercomputer Center, and the University of California, San Diego.1 MIXm uses XML as the common model for data exchange. Mediator views are expressed in XMAS (XML Matching And Structuring Language), a declarative XML query language. To facilitate user-friendly query formulation and for optimization purposes, MIXm employs XML DTDs as a structural description (in effect, a “schema”) of the exchanged data. The novel features of the system include: