A better subgraph of the minimum weight triangulation

1995 ◽  
pp. 452-455 ◽  
Author(s):  
Bo-Ting Yang
Keyword(s):  
Minimum Weight ◽  
Minimum Weight Triangulation

scholarly journals On a Linear Program for Minimum-Weight Triangulation

2014 ◽  
Vol 43 (1) ◽  
pp. 25-51 ◽  
Author(s):  
Arman Yousefi ◽  
Neal E. Young
Keyword(s):  
Minimum Weight ◽  
Linear Program ◽  
Minimum Weight Triangulation

scholarly journals Polynomial-time instances of the minimum weight triangulation problem

1993 ◽  
Vol 3 (5) ◽  
pp. 247-259 ◽  
Author(s):  
Efthymios Anagnostou ◽  
Derek Corneil
Keyword(s):  
Polynomial Time ◽  
Minimum Weight ◽  
Minimum Weight Triangulation

Minimum Weight Triangulation

2008 ◽  
pp. 546-548
Author(s):  
Christos Levcopoulos
Keyword(s):  
Minimum Weight ◽  
Minimum Weight Triangulation

scholarly journals On β-skeleton as a subgraph of the minimum weight triangulation

2001 ◽  
Vol 262 (1-2) ◽  
pp. 459-471 ◽  
Author(s):  
Siu-Wing Cheng ◽  
Yin-Feng Xu
Keyword(s):  
Minimum Weight ◽  
Minimum Weight Triangulation

DIAMONDS ARE NOT A MINIMUM WEIGHT TRIANGULATION'S BEST FRIEND

2002 ◽  
Vol 12 (06) ◽  
pp. 445-453 ◽  
Author(s):  
PROSENJIT BOSE ◽  
LUC DEVROYE ◽  
WILLIAM EVANS
Keyword(s):  
Polynomial Time ◽  
Minimum Weight ◽  
Connected Subgraph ◽  
Constant Number ◽  
Point Sets ◽  
Expected Number ◽  
Number Of Components ◽  
Best Friend ◽  
Point Set ◽  
Minimum Weight Triangulation

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.

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