The existence problem for Steiner networks in strictly convex domains
Alex Freire (University of Tennessee Knoxville)
TL;DR
This paper investigates the conditions under which Steiner networks, which are trivalent graphs with 120-degree angles, can exist within strictly convex domains, providing both existence criteria and explicit nonexistence examples.
Contribution
It establishes sufficient conditions for the existence of Steiner networks in convex domains and presents explicit examples where such networks do not exist.
Findings
Derived sufficient conditions for Steiner network existence.
Provided explicit nonexistence examples.
Analyzed all three combinatorial possibilities.
Abstract
We consider the existence problem for `Steiner networks' (trivalent graphs with 120 degree angles at each junction) in strictly convex domains, with `Neumann' boundary conditions (orthogonal intersection with the domain boundary.) For each of the three possible combinatorial possibilities, sufficient conditions on the domain are derived for existence; in addition, in each case explicit examples of nonexistence are given.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsTopology Optimization in Engineering · VLSI and FPGA Design Techniques · Interconnection Networks and Systems