Matic Mercina (2012) *Computing minimum weight triangulation*. EngD thesis.

## Abstract

The thesis describes point set triangulation in a real plane, and deals with the minimum weight triangulation problem in more detail. Due to the NP-completeness of the problem, the following question arises: is it necessary to know the exact solution for the given point set, or is a close approximation enough? As we increase the size of the problem, we begin leaning towards the second option, due mainly to the fact that an NP-complete problem simply cannot be solved in sufficient time on large inputs. For the above reasons, we present a divide and conquer algorithm, which first calculates an arbitrary triangulation for the given input, and then gradually improves the result by switching connections. The implemented solution allows for different modes of operation based on methods of subdivision and methods of improvement. The results show which operating mode is the fastest, what are the differences in the final solutions, and what is the time complexity of the algorithm.

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