Efficient maintenance of the union intervals on a line, with applications

Siu Wing Cheng, Ravi Janardan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

We consider the problem of maintaining, under insertions and deletions, the union of a set S of intervals on a line. We present a scheme that reports the ordered list of intervals in the union in Θ(k) time, while achieving O(logn) time in worst case for each insertion or deletion, where n is the number of intervals currently in S and k is the number of disjoint intervals in the union. The scheme uses 0(n) space. This is an improvement upon a previous approach [7] which uses O(log2 n) time for each insertion or deletion. One of the applications of our scheme is an optimal contour algorithm for iso-oriented rectangles that is simpler and more practical than a previous optimal algorithm [4].

Original languageEnglish (US)
Title of host publicationProceedings of the 1st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1990
PublisherAssociation for Computing Machinery
Pages74-83
Number of pages10
ISBN (Electronic)0898712513
StatePublished - Jan 1 1990
Event1st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1990 - San Francisco, United States
Duration: Jan 22 1990Jan 24 1990

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Other

Other1st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1990
CountryUnited States
CitySan Francisco
Period1/22/901/24/90

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