Efficient hidden surface removal for objects with small union size
Computational Geometry: Theory and Applications
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
Proceedings of the twenty-second annual symposium on Computational geometry
Smoothed analysis of probabilistic roadmaps
Computational Geometry: Theory and Applications
I/O-Efficient flow modeling on fat terrains
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Complexity analysis of random geometric structures made simpler
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We study the complexity of the visibility map of terrains whose triangles are fat, not too steep and have roughly the same size. It is known that the complexity of the visibility map of such a terrain with n triangles is θ(n2) in the worst case. We prove that if the elevations of the vertices of the terrain are subject to uniform noise which is proportional to the edge lengths, then the worst-case expected (smoothed) complexity is only θ(n). This provides an explanation why visibility maps of superlinear complexity are unlikely to be encountered in practice.