Proceedings of the twenty-second annual symposium on Computational geometry
A Constant-Factor Approximation Algorithm for Optimal 1.5D Terrain Guarding
SIAM Journal on Computing
A 4-approximation algorithm for guarding 1.5-dimensional terrains
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Flooding countries and destroying dams
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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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.