We present an O(n log n)-time algorithm to solve the three-dimensional layers-of-maxima problem, 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, Goodrich, and Ramaiyer [SCG’94] 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.
CITATION STYLE
Buchsbaum, A. L., & Goodrich, M. T. (2002). Three-dimensional layers of maxima. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2461, pp. 257–269). Springer Verlag. https://doi.org/10.1007/3-540-45749-6_26
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