Towards Optimal Indexing for Segment Databases

. Segment databases store N non-crossing but possibly touching segments in secondary storage. Efficient data structures have been proposed to determine all segments intersecting a vertical line (stabbing queries). In this paper, we consider a more general type of query for segment databases, determining intersections with respect to a generalized segment (a line, a ray, a segment) with a fixed angular coefficient. We propose two solutions to solve this problem. The first solution has optimal O( N B ) space complexity, where N is the database size and B is the page size, but the query time is far from optimal. The second solution requires O( N B log 2 B) space, the query time is O(log B N B (log B N B +log 2 B+ IL (B)) + T B ), which is very close to the optimal, and insertion amortized time is O(log B N B + log 2 B + 1 B log 2 B N B ), where T is the size of the query result, and IL (B) is a small constant, representing the number of times we must repeatedly apply the log..