Optimal algorithms to compute the closure of a set of iso-rectangles

doi:10.1016/0196-6774(84)90027-0

Journal of Algorithms

Volume 5, Issue 2, June 1984, Pages 199-214

https://doi.org/10.1016/0196-6774(84)90027-0 Get rights and content

Abstract

Three varieties of the closure of a set of iso-(oriented) rectangles, i.e., rectilin-early-oriented rectangles, are introduced. These are uni-directional, diagonal, and rectangular closure. First a strong decomposition theorem for diagonal closure in terms of uni-directional closure is proved. Then time and space optimal algorithms to compute uni-directional and diagonal closure, each running in O(nlogn) time and O(n) space, are described. An O(nlogn) time and space algorithm for rectangular closure is also described. The algorithm for diagonal closure has applications in database concurrency control: an O(nlogn) time and O(n) space algorithm for testing for safety and detecting deadlocks in locked transaction systems is obtained.

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^☆: The work of the second author was partially supported by a Natural Sciences and Engineering Research Council of Canada Grant A-7700 and was carried out while visiting the University of Helsinki. Some of the work of the first author was conducted while visiting the University of Karlsruhe under the support of the Alexander von Humboldt Foundation. Some of the results were also presented in preliminary form at the ACM SIGACT-SIGMOD Conference on Principles of Database Systems, Los Angeles, March 1982.

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Optimal algorithms to compute the closure of a set of iso-rectangles☆

Abstract

J. Algorithms

The Design and Analysis of Computer Algorithms

Algorithms for reporting and counting geometric intersections

IEEE Transactions on Computers

The notions of consistency and predicate locks in a database system

Communications of the ACM