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Computer Science > Data Structures and Algorithms

arXiv:2309.10122 (cs)
[Submitted on 18 Sep 2023 (v1), last revised 28 May 2024 (this version, v2)]

Title:Graph Threading

Authors:Erik D. Demaine, Yael Kirkpatrick, Rebecca Lin
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Abstract: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.
Comments: 19 pages, 6 figures
Subjects: Data Structures and Algorithms (cs.DS)
ACM classes: G.2.2; F.2.2
Cite as: arXiv:2309.10122 [cs.DS]
  (or arXiv:2309.10122v2 [cs.DS] for this version)
  https://doi.org/10.48550/arXiv.2309.10122
Related DOI: https://doi.org/10.4230/LIPIcs.ITCS.2024.38

Submission history

From: Rebecca Lin [view email]
[v1] Mon, 18 Sep 2023 19:51:58 UTC (5,238 KB)
[v2] Tue, 28 May 2024 08:31:05 UTC (5,447 KB)
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