# Item

ITEM ACTIONSEXPORT

Released

Conference Paper

#### Linear-Time Triangulation of a Simple Polygon Made Easier Via Randomization

##### Locator

There are no locators available

##### Fulltext (public)

There are no public fulltexts available

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Amato, N. M., Goodrich, M. T., & Ramos, E. A. (2000). Linear-Time Triangulation
of a Simple Polygon Made Easier Via Randomization. In *Proceedings of the 16th Annual Symposium on
Computational Geometry (SCG-00)* (pp. 201-212). New York, USA: ACM Press.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-33D1-4

##### Abstract

We describe a randomized algorithm for computing the trapezoidal decomposition
of a simple polygon. Its expected running time is linear in the size of the
polygon.
By a well-known and simple linear time reduction, this implies a linear time
algorithm for triangulating a simple polygon. Our algorithm is considerably
simpler
than Chazelle's (1991) celebrated optimal deterministic algorithm
and, hence, positively answers his question of whether a simpler randomized
algorithm for the problem exists. The new algorithm can be viewed as a
combination
of Chazelle's algorithm and of non-optimal randomized algorithms due to Clarkson
{\it et al.} (1991) and to Seidel (1991), with the essential innovation that
sampling
is performed on subchains of the initial polygonal chain, rather than on its
edges.
It is also essential, as in Chazelle's algorithm, to include a bottom-up
preprocessing phase previous to the top-down construction phase.