Numerical Calibration of Steiner trees
- 78 Downloads
In this paper we propose a variational approach to the Steiner tree problem, which is based on calibrations in a suitable algebraic environment for polyhedral chains which represent our candidates. This approach turns out to be very efficient from numerical point of view and allows to establish whether a given Steiner tree is optimal. Several examples are provided.
KeywordsCalibration Minimal surface Steiner tree problem
Mathematics Subject Classification49J45 35R35 49M05 35J25
We would like to thank the MmgTools team (see https://github.com/MmgTools/mmg): Charles Dapogny, Cécile Dobrzynski, Pascal Frey and Algiane Froehly) for providing the remeshing software required to generate constraint meshes. Édouard Oudet gratefully acknowledges the support of the ANR, through the projects COMEDIC, GEOMETRYA, PGMO and OPTIFORM.
- 5.Karp, R.M.: Reducibility among combinatorial problems, Complexity of computer computations In: Proceedings Symposium, IBM Thomas J. Watson Res. Center, pp. 85–103 Yorktown Heights, NY (1972)Google Scholar
- 7.Warme, D.M., Winter, P., Zachariasen, M.: GeoSteiner 3.1 Department of Computer Science. University of Copenhagen (DIKU), Copenhagen (2001)Google Scholar