Kinetic and dynamic data structures for convex hulls and upper envelopes

Giora Alexandron*, Haim Kaplan, Micha Sharir

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review


Let S be a set of n moving points in the plane. We present a kinetic and dynamic (randomized) data structure for maintaining the convex hull of S. The structure uses O(n) space, and processes an expected number of O(n 2βs+2(n) log n) critical events, each in O(log 2 n) expected time, including O(n) insertions, deletions, and changes in the flight plans of the points. Here s is the maximum number of times where any specific triple of points can become collinear, βs(q) = λs(q)/q, and λs (q) is the maximum length of Davenport-Schinzel sequences of order s on n symbols. Compared with the previous solution of Basch et al. [2], our structure uses simpler certificates, uses roughly the same resources, and is also dynamic.

Original languageEnglish
Pages (from-to)269-281
Number of pages13
JournalLecture Notes in Computer Science
StatePublished - 2005
Event9th International Workshop on Algorithms and Data Structures, WADS 2005 - Waterloo, Canada
Duration: 15 Aug 200517 Aug 2005


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