Dynamic Maintenance of Maxima of 2-d Point Sets

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Dynamic Maintenance of Maxima of 2-d Point Sets
This paper describes an efficient scheme for the dynamic maintenance of the set of maxima of a 2-d set of points. Using the fact that the maxima can be stored in a staircase structure, we use a technique in which we maintain approximations to the staircase structure. We first describe how to maintain the maxima in O(log n) time per insertion and deletion when there are n insertions and deletions. O(log n) is charged per change for reporting changes to the staircase structure which stores the maxima. O(n) space is used. We also show another scheme which requires a total of O(n log n + r) time when r maximal points are listed. We finally consider extensions to higher dimensions. Key words. maximal points, dynamic maintenance, balanced trees AMS subject classifications. 68Q25, 68U05, 68P05 PII. S0097539798348365
Sanjiv Kapoor
Added 19 Dec 2010
Updated 19 Dec 2010
Type Journal
Year 2000
Authors Sanjiv Kapoor
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