Journal of Global Optimization

, 46:63

A new asymmetric inclusion region for minimum weight triangulation


DOI: 10.1007/s10898-009-9409-z

Cite this article as:
Hu, S. J Glob Optim (2010) 46: 63. doi:10.1007/s10898-009-9409-z


As a global optimization problem, planar minimum weight triangulation problem has attracted extensive research attention. In this paper, a new asymmetric graph called one-sided β-skeleton is introduced. We show that the one-sided circle-disconnected \({(\sqrt{2}\beta)}\) -skeleton is a subgraph of a minimum weight triangulation. An algorithm for identifying subgraph of minimum weight triangulation using the one-sided \({(\sqrt{2}\beta)}\) -skeleton is proposed and it runs in \({O(n^{4/3+\epsilon}+\min\{\kappa \log n, n^2\log n\})}\) time, where κ is the number of intersected segmented between the complete graph and the greedy triangulation of the point set.


Minimum weight triangulationInclusion regionOne-sided β-skeleton

Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringMichigan Technological UniversityHoughtonUSA