Proceedings of 37th Conference on Foundations of Computer Science (1996)
Oct. 14, 1996 to Oct. 16, 1996
L. Arge , Dept. of Comput. Sci., Duke Univ., Durham, NC, USA
J.S. Vitter , Dept. of Comput. Sci., Duke Univ., Durham, NC, USA
The authors present a space- and I/O-optimal external-memory data structure for answering stabbing queries on a set of dynamically maintained intervals. The data structure settles an open problem in databases and I/O algorithms by providing the first optimal external-memory solution to the dynamic interval management problem, which is a special case of 2-dimensional range searching and a central problem for object-oriented and temporal databases and for constraint logic programming. The data structure simultaneously uses optimal linear space (that is, O(N/B) blocks of disk space) and achieves the optimal O(log/sub B/ N+T/B) I/O query bound and O(log/sub B/ N) I/O update bound, where B is the I/O block size and T the number of elements in the answer to a query. The structure is also the first optimal external data structure for a 2-dimensional range searching problem that has worst-case as opposed to amortized update bounds. Part of the data structure uses a novel balancing technique for efficient worst-case manipulation of balanced trees, which is of independent interest.
storage management; optimal dynamic interval management; external memory; space-optimal external-memory data structure; I/O-optimal external-memory data structure; stabbing query answering; dynamically maintained intervals; databases; I/O algorithms; 2D range searching; temporal databases; object-oriented databases; constraint logic programming; optimal linear space; optimal I/O query bound; optimal I/O update bound; worst-case update bounds; balancing technique; worst-case balanced tree manipulation
L. Arge and J. Vitter, "Optimal dynamic interval management in external memory," Proceedings of 37th Conference on Foundations of Computer Science(FOCS), Burlington, VT, 1996, pp. 560.