The interval skip list: A data structure for finding all intervals that overlap a point
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A problem that arises in computational geometry, pattern matching, and other applications is the need to quickly determine which of a collection of intervals overlap a query point. The interval binary search tree (IBS-tree) has been proposed as a solution to this problem. A recently discovered randomized data structure called the skip list provides functionality and performance similar to balanced binary trees (e.g., AVL-trees), but is much simpler to implement than balanced trees. This paper introduces an extension of the skip list called the interval skip list, or IS-list, to support interval indexing. IS-lists remain dynamicly balanced, and show similar performance to IBS-trees, but can be implemented in about one-fourth as much high-level language code. Searching an IS-list containing n intervals to find intervals overlapping a point takes expected time O(log n+L) where L is the number of matching intervals. Inserting or deleting an mterval takes expected time O(log2n).
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- [AVL62]G. M. Adel'son-Vel'skii and E. M. Landis. An algorithm for the organization of information. Soviet Math. Dokl., 3, 1962.Google Scholar
- [Ede83a]H. Edelsbrunner. A new approach to rectangle intersections: Part I. International Journal of Computer Mathematics, 13(3–4):209–219, 1983.Google Scholar
- [Ede83b]H. Edelsbrunner. A new approach to rectangle intersections: Part II. International Journal of Computer Mathematics, 13(3–4):221–229, 1983.Google Scholar
- [GMW83]Gaston H. Gonnet, J. Ian Munro, and Derick Wood. Direct dynamic structures for some line segment problems. Computer Vision, Graphics, and Image Processing, 23, 1983.Google Scholar
- [Gut84]A. Guttman. R-trees: A dynamic index structure for spatial searching. In Proceedings of the 1984 ACM SIGMOD International Conference on Management of Data, June 1984.Google Scholar
- [Han89]Eric N. Hanson. An initial report on the design of Ariel: a DBMS with an integrated production rule system. SIGMOD Record, 18(3), September 1989.Google Scholar
- [HC90]Eric N. Hanson and Moez Chaabouni. The IBS-tree: A data structure for finding all intervals that overlap a point. Technical Report WSU-CS-90-11, Dept. of Computer Science and Eng., Wright State Univ., April 1990. Submitted for publication.Google Scholar
- [HCKW90]Eric N. Hanson, Moez Chaabouni, Chang-ho Kim, and Yu-wang Wang. A predicate matching algorithm for database rule systems. In Proceedings of the 1990 ACM SIGMOD International Conference on Management of Data, May 1990.Google Scholar
- [McC85]Edward M. McCreight. Priority search trees. SIAM Journal of Computing, 14(2):257–278, 1985.Google Scholar
- [Pug89]William Pugh. A skip list cookbook. Technical Report CS-TR-2286, Dept. of Computer Science, Univ. of Maryland, July 1989.Google Scholar
- [Pug90]William Pugh. Skip lists: A probabilistic alternative to balanced trees. Communications of the ACM, 33(6), June 1990.Google Scholar
- [Sam90]Hanan Samet. The Design and Analysis of Spatial Data Structures. Addision Wesley, 1990.Google Scholar