Open problems on Steiner trees and maximal distance minimizers
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914168240603136 |
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| author | Teplitskaya, Yana |
| author_facet | Teplitskaya, Yana |
| contents | 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 $r$-neighborhood covers a given compact set, whereas Steiner trees aim to find a minimal-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18217 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Open problems on Steiner trees and maximal distance minimizers Teplitskaya, Yana Metric Geometry 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 $r$-neighborhood covers a given compact set, whereas Steiner trees aim to find a minimal-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. |
| title | Open problems on Steiner trees and maximal distance minimizers |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2511.18217 |