Graph Threading
Fuente:
arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866929361242816512 |
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| author | Demaine, Erik D. Kirkpatrick, Yael Lin, Rebecca |
| author_facet | Demaine, Erik D. Kirkpatrick, Yael Lin, Rebecca |
| contents | Inspired by artistic practices such as beadwork and himmeli, we study the problem of threading a single string through a set of tubes, so that pulling the string forms a desired graph. More precisely, given a connected graph (where edges represent tubes and vertices represent junctions where they meet), we give a polynomial-time algorithm to find a minimum-length closed walk (representing a threading of string) that induces a connected graph of string at every junction. The algorithm is based on a surprising reduction to minimum-weight perfect matching. Along the way, we give tight worst-case bounds on the length of the optimal threading and on the maximum number of times this threading can visit a single edge. We also give more efficient solutions to two special cases: cubic graphs and the case when each edge can be visited at most twice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10122 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Graph Threading Demaine, Erik D. Kirkpatrick, Yael Lin, Rebecca Data Structures and Algorithms G.2.2; F.2.2 Inspired by artistic practices such as beadwork and himmeli, we study the problem of threading a single string through a set of tubes, so that pulling the string forms a desired graph. More precisely, given a connected graph (where edges represent tubes and vertices represent junctions where they meet), we give a polynomial-time algorithm to find a minimum-length closed walk (representing a threading of string) that induces a connected graph of string at every junction. The algorithm is based on a surprising reduction to minimum-weight perfect matching. Along the way, we give tight worst-case bounds on the length of the optimal threading and on the maximum number of times this threading can visit a single edge. We also give more efficient solutions to two special cases: cubic graphs and the case when each edge can be visited at most twice. |
| title | Graph Threading |
| topic | Data Structures and Algorithms G.2.2; F.2.2 |
| url | https://arxiv.org/abs/2309.10122 |