ISSN:
1432-0541
Keywords:
Geometric algorithms
;
Grid generation
;
Regular and Delaunay triangulations
;
Flipping
;
Topological order
;
Point location
;
Incremental
;
Randomized
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract A set ofn 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 mostO(nlogn+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 logn 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01975867
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