Quasi-greedy triangulations approximating the minimum weight triangulation
- Lund Univ. (Sweden)
This paper settles the following two open problems: (1) What is the worst-case approximation ratio between the greedy and the minimum weight triangulation? (2) Is there a polynomial time algorithm that always pro- duces a triangulation whose length is within a constant factor from the minimum? The answer to the first question is that the known {Omega}({radical}n) lower bound is tight. The second question is answered in the affirmative by using a slight modification of an O(n log n) algorithm for the greedy triangulation. We also derive some other interesting results. For example, we show that a constant-factor approximation of the minimum weight convex partition can be obtained within the same time bounds.
- OSTI ID:
- 416823
- Report Number(s):
- CONF-960121-; TRN: 96:005887-0046
- Resource Relation:
- Conference: 7. annual ACM-SIAM symposium on discrete algorithms, Atlanta, GA (United States), 28-30 Jan 1996; Other Information: PBD: 1996; Related Information: Is Part Of Proceedings of the seventh annual ACM-SIAM symposium on discrete algorithms; PB: 596 p.
- Country of Publication:
- United States
- Language:
- English
Similar Records
Refining a triangulation of a planar straight-line graph to eliminate large angles
Limit theorems for minimum-weight triangulations, other euclidean functionals, and probabilistic recurrence relations