Branching points in the planar Gilbert--Steiner problem have degree 3
Danila Cherkashin, Fedor Petrov
TL;DR
This paper proves that in the planar Gilbert--Steiner problem, all branching points in optimal solutions have degree 3, clarifying the structure of these solutions.
Contribution
It establishes that every branching point in the planar Gilbert--Steiner problem solution has degree 3, a new structural property.
Findings
All branching points have degree 3 in planar solutions.
Provides a structural characterization of solutions.
Enhances understanding of optimal mass transportation networks.
Abstract
Gilbert--Steiner problem is a generalization of the Steiner tree problem on a specific optimal mass transportation. We show that every branching point in a solution of the planar Gilbert--Steiner problem has degree 3.
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Taxonomy
TopicsAdvanced Graph Theory Research · VLSI and FPGA Design Techniques · Advanced Optical Network Technologies