Journal of convex analysis· 2026Q2
Open problems on Steiner trees and maximal distance minimizers
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- Q2SCImago
- 2026year
Short summary
This paper outlines open research questions in one-dimensional geometric optimization, specifically focusing on maximal distance minimizers and Steiner trees in Euclidean spaces.
AI-generated from the title and abstract; the full text is not read.
Key points
- Identifies open research questions in 1D geometric optimization.
- Focuses on maximal distance minimizers and Steiner trees.
- Summarizes known results and remaining challenges for both problem classes.
- Notes that some open questions are approachable with basic methods, while others are highly complex.
AI-generated from the title and abstract; the full text is not read.
Abstract
In this work, I collect and discuss a series of open questions in one-dimensional geometric optimization in Euclidean spaces. The focus is on two classes of problems: maximal distance minimizers and Steiner trees. Maximal distance minimizers concern finding a connected set of minimal length whose closed r r -neighborhood covers a given compact set, whereas Steiner trees aim to find a minimum-length set connecting a prescribed set of points. For both problems, I briefly summarize known results and highlight the remaining open questions. While some questions can be approached with elementary methods, others remain highly challenging.
The authors' abstract, as published at the source. Journal of convex analysis, 2026 · DOI ↗
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Field: Computer Graphics and Computer-Aided Design
Computer Graphics and Computer-Aided DesignComputer Science