Dynamic maintenance of maximas of 2-d point sets

Authors:
Sanjiv Kapoor
Affiliations:
Department of Computer Science, Indian Institute of Technology, Hauz Khas, New Delhi 110016
Venue:
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Year:
1994

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Abstract

This paper describes an efficient scheme to dynamically maintain the set of maximas of a 2-d set of points. Using the fact that the maximas can be stored in a Staircase structure, we use a technique which maintains approximations to the Staircase structure. We first show how to maintain the maximas in O(logn) time per insertion and deletion when there are n insertions and deletions. O(logn) is charged per change for reporting changes to the structure. We also show another scheme which requires O(logn) amortized time per insertion and deletion with an output complexity of O(r) steps when r maximal points are to be listed. The data structures require O(n) space.