The point-range tree: a data structure for indexing intervals

Authors:
Moez Chaabouni;Soon M. Chung
Affiliations:
Department of Computer Science and Engineering, Wright State University, Dayton, Ohio;Department of Computer Science and Engineering, Wright State University, Dayton, Ohio
Venue:
CSC '93 Proceedings of the 1993 ACM conference on Computer science
Year:
1993

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Abstract

In this paper, we propose a data structure, the Point-Range Tree (PR-Tree), specifically designed for indexing intervals. With the PR-Tree, a point data can be queried against a set of intervals to determine which of those intervals overlap the point. The PR-tree allows dynamic insertions and deletions while it maintains itself balanced. A balanced PR-Tree takes &Ogr;(log n) time for search. Insertion, deletion, and storage space have worst case requirements of &Ogr;(n log n + m), &Ogr;(n log2 n + m), and &Ogr;(n log n), respectively, where n is the total number of intervals in the tree, and m the number of nodes visited during insertion and deletion. A modified version of the PR-Tree is also developed to minimize space usage. An additional advantage of the PR-Tree is that it can be easily extended to multi-dimensional domains.