Organizing and indexing non-convex regions

We demonstrate data indexing and query processing techniques that improve the efficiency of comparing, correlating, and joining data contained in non-convex regions. We use computational geometry techniques to automatically characterize the region of space from which data are drawn, partition the region based on that characterization, and create an index from the partitions. Our motivating application performs distributed data analysis queries among federated database sites that store scientific data sets from the Chesapeake Bay. Our preliminary findings indicate that these techniques often reduce the number of I/Os needed to serve a query by a factor of five—depending on the geometry of the query region. Our approach automatically extracts the structure of the region to facilitate data organization and query processing. We use an approximate medial axis transform to discover and describe the region. The medial axis is generated using a constrained Delaunay triangulation [3]. We represent the medial axis as a tree and enumerate the nodes of the tree to generate the labels for our spatial index. The index defines a linear order on the Delaunay triangles. Data from each triangle are then placed on disk in index order, e.g. using a B+-tree. When using this index, structures (in our case, estuaries, rivers, and bays) occupy contiguous regions of the index, which makes the data from these regions contiguous on disk. We will demonstrate an interactive application in which the user can select from a variety of shape files, including the Chesapeake Bay, other estuaries, and artificial shapes. The demo will show the generation of an index, including the Delaunay triangulation and medial axis transform. The user will then select query regions in the space and the demo will show both the portions of the index associated with these regions and, for the Chesapeake Bay, the data layout on disk for multiple data sets. The demo will compare the index regions and data layout among our medial axis index and regular spatial decompositions, such as region trees, tessellations, and space filling curves.