Chapter

Towards optimal indexing for segment databases

12/2006; DOI:10.1007/BFb0100976 pp.39-53

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 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 log2
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+log2
B+1/Blog2
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* function to B before the result becomes ≤ 2.

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Keywords

angular coefficient
 
B+IL
 
database size
 
Efficient data structures
 
first solution
 
generalized segment
 
insertion amortized time
 
intersections
 
log* function
 
optimal
 
page size
 
query result
 
query time
 
segment databases
 
Segment databases store N non-crossing
 
segments
 
segments intersecting
 
small constant
 
vertical line