On Nonlinear Parametric Search

Abstract.

An alternative viewpoint for parametric search is presented, which achieves a bound similar to that of Cole's improvement on Megiddo's method. The new technique simulates the algorithm for the underlying fixed-parameter problem simultaneously over multiple computation paths and applies naturally to linear and nonlinear problems. The uses of the method are illustrated with examples from optimization on weighted graphs and dynamic geometry, including maximum spanning trees, diameter, and smallest enclosing ball.