Towards optimal indexing for segment databases

Abstract

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 fine, 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/Blog2 B) space, the query time is O(logB N/B(logB N/B+ log2 B + IL*(B)) + T/B), which is very close to the optimal, and insertion amortized time is O(logB N/B+ log2B + 1/B log B2 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* function to B before the result becomes ≤ 2.