# Incremental topological flipping works for regular triangulations

- Received:
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DOI: 10.1007/BF01975867

- Cite this article as:
- Edelsbrunner, H. & Shah, N.R. Algorithmica (1996) 15: 223. doi:10.1007/BF01975867

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## Abstract

A set of*n* weighted points in general position in ℝ^{d} defines a unique regular triangulation. This paper proves that if the points are added one by one, then flipping in a topological order will succeed in constructing this triangulation. If, in addition, the points are added in a random sequence and the history of the flips is used for locating the next point, then the algorithm takes expected time at most*O(n*log*n+n*^{[d/2]}). Under the assumption that the points and weights are independently and identically distributed, the expected running time is between proportional to and a factor log*n* more than the expected size of the regular triangulation. The expectation is over choosing the points and over independent coin-flips performed by the algorithm.