Approximation and Online Algorithms

Volume 5426 of the series Lecture Notes in Computer Science pp 214-226

Smoothing Imprecise 1.5D Terrains

  • Chris GrayAffiliated withDepartment of Computer Science, TU Braunschweig
  • , Maarten LöfflerAffiliated withDept. Computer Science, Utrecht University
  • , Rodrigo I. SilveiraAffiliated withDept. Computer Science, Utrecht University

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We study optimization problems in an imprecision model for polyhedral terrains. An imprecise terrain is given by a triangulated point set where the height component of the vertices is specified by an interval of possible values. We restrict ourselves to 1.5-dimensional terrains: an imprecise terrain is given by an x-monotone polyline, and the y-coordinate of each vertex is not fixed but constrained to a given interval. Motivated by applications in terrain analysis, in this paper we present two linear-time approximation algorithms, for minimizing the largest turning angle and for maximizing the smallest one. In addition, we also provide linear time exact algorithms for minimizing and maximizing the sum of the turning angles.