Towards Optimal Indexing for Segment Databases

Segment databases store N non-crossing but possibly touching segments in secondary storage. EEcient 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 xed angular coeecient. We propose two solutions to solve this problem. The rst 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 + I L (B)) + T B), which is very close to the optimal, and insertion amort-ized 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 I L (B) is a small constant, representing the number of times we must repeatedly apply the log function to B before the result becomes 2.