Abstract
We consider the following planar maximum weight triangulation (MAT) problem: given a set of n points in the plane, find a triangulation such that the total length of edges in triangulation is maximized. We prove an \(\Omega(\sqrt{n})\) lower bound on the approximation factor for several heuristics: maximum greedy triangulation, maximum greedy spanning tree triangulation and maximum spanning tree triangulation. We then propose the Spoke Triangulation algorithm, which approximates the maximum weight triangulation for points in general position within a factor of almost four in O(nlog n) time. The proof is simpler than the previous work. We also prove that Spoke Triangulation approximates the maximum weight triangulation of a convex polygon within a factor of two.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
