Abstract
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(log2 n).
This work was supported by the Air Force Office of Scientific Research under grant number AFOSR-89-0286.
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References
G. M. Adel'son-Vel'skii and E. M. Landis. An algorithm for the organization of information. Soviet Math. Dokl., 3, 1962.
H. Edelsbrunner. A new approach to rectangle intersections: Part I. International Journal of Computer Mathematics, 13(3–4):209–219, 1983.
H. Edelsbrunner. A new approach to rectangle intersections: Part II. International Journal of Computer Mathematics, 13(3–4):221–229, 1983.
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.
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.
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.
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.
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.
Edward M. McCreight. Priority search trees. SIAM Journal of Computing, 14(2):257–278, 1985.
William Pugh. A skip list cookbook. Technical Report CS-TR-2286, Dept. of Computer Science, Univ. of Maryland, July 1989.
William Pugh. Skip lists: A probabilistic alternative to balanced trees. Communications of the ACM, 33(6), June 1990.
Hanan Samet. The Design and Analysis of Spatial Data Structures. Addision Wesley, 1990.
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© 1991 Springer-Verlag Berlin Heidelberg
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Hanson, E.N. (1991). The interval skip list: A data structure for finding all intervals that overlap a point. In: Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1991. Lecture Notes in Computer Science, vol 519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028258
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DOI: https://doi.org/10.1007/BFb0028258
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