Three-Dimensional Layers of Maxima

Abstract. We present an O(n log n)-time algorithm to solve the threedimensional 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.

• Type: Journal
• Year: 2004
• Where: ALGORITHMICA
• Authors: Adam L. Buchsbaum, Michael T. Goodrich
• Keywords: Algorithm, ALGORITHMICA 2004, Dynamic Planar Point, Threedimensional Layers-of-maxima Problem