- View PDF version of TR-96-01 (138644 bytes)
- View PostScript version of TR-96-01
- Save PostScript version of TR-96-01
- Save gzipped PostScript version of TR-96-01 (42562 bytes)

- Diamonds are not a Minimum Weight Triangulation's Best Friend, January 1996 Prosenjit Bose, Luc Devroye and William Evans, 10 pages
Two recent methods have increased hopes of finding a polynomial time solution to the problem of computing the minimum weight triangulation of a set $S$ of $n$ points in the plane. Both involve computing what was believed to be a connected or nearly connected subgraph of the minimum weight triangulation, and then completing the triangulation optimally. The first method uses the light graph of $S$ as its initial subgraph. The second method uses the \lmt-skeleton of $S$. Both methods rely, for their polynomial time bound, on the initial subgraphs having only a constant number of components. Experiments performed by the authors of these methods seemed to confirm that randomly chosen point sets displayed this desired property. We show that there exist point sets where the number of components is linear in $n$. In fact, the expected number of components in either graph on a randomly chosen point set is linear in $n$, and the probability of the number of components exceeding some constant times $n$ tends to one.

If you have any questions or comments regarding this page please send mail to help@cs.ubc.ca.