In-Place Algorithms for Computing (Layers of) Maxima

Authors:
Henrik Blunck;Jan Vahrenhold
Affiliations:
University of Århus, MADALGO (Center for Massive Data Algorithmics, a Center of the Danish National Research Foundation), Department of Computer Science, 8200, Aarhus, Denmark;Technische Universität Dortmund, Informatik XI, 44221, Dortmund, Germany
Venue:
Algorithmica - Including a Special Section on Genetic and Evolutionary Computation; Guest Editors: Benjamin Doerr, Frank Neumann and Ingo Wegener
Year:
2010

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Abstract

We describe space-efficient algorithms for solving problems related to finding maxima among points in two and three dimensions. Our algorithms run in optimal $\mathcal{O}(n\log n)$time and occupy only constant extra space in addition to the space needed for representing the input.