Some Lower Bounds on Geometric Separability Problems

We obtain lower bounds in the algebraic computation tree model for deciding the separability of two disjoint point sets. In particular, we show (n log n) time lower bounds for separability by means of strips, wedges, wedges with apices on a given line, fixed-slopes double wedges, and triangles, which match the complexity of the existing algorithms, and therefore prove their optimality. Key Words: Lower bounds; separation; maximum gap.

• Type: Journal
• Year: 2006
• Where: IJCGA
• Authors: Esther M. Arkin, Ferran Hurtado, Joseph S. B. Mitchell, Carlos Seara, Steven Skiena
• Keywords: Algebraic Computation Tree, Disjoint Point Sets, IJCGA 2006, Lower Bounds