An efficient external-memory implementation of region query with application to area routing

We present the tile-cached kd-tree, an efficient external-memory (disk) implementation of two-dimensional region query for use in a detailed area router. Most researchers have heretofore focused on in-memory algorithms. However as the need to tackle very large problems increases, conventional in-memory algorithms suffer from unpredictable caching and paging behavior and their performance may degrade considerably. In addition, since the region-query data structure is only part of the overall system, its consumption of large memory resources affects other parts of the system as well. Our implementation takes advantage of spatial locality in the detailed-routing process. We partition the routing space into tiles, each storing the data of objects (rectangles) that lie strictly within it. Objects that cross tile boundaries are separately stored. The data within a tile are then written out to disk, and a configurable cache is used to hold in memory the most recently visited tiles. Experimental results on large real-life routing problems show that this scheme significantly reduces memory usage with tolerable performance penalty.