Three-Dimensional Layers of Maxima

Authors:
Adam L. Buchsbaum;Michael T. Goodrich
Affiliations:
AT&T Labs, Shannon Laboratory, 180 Park Ave., Florham Park, NJ 07932, USA;Department of Information and Computer Science, University of California, Irvine, CA 92697-3425, USA
Venue:
Algorithmica
Year:
2004

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Abstract

We present an O(n log n)-time algorithm to solve the three-dimensional layers-of-maxima problem. This is an improvement over the prior O(n log n log log n)-time solution. A previous claimed O(n log n)-time solution due to Atallah et al. has technical flaws. Our algorithm is based on a common framework underlying previous work, but to implement it we devise a new data structure to solve a special case of dynamic planar point location in a staircase subdivision. Our data structure itself relies on a new extension to dynamic fractional cascading that allows vertices of high degree in the control graph.