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Graph Threading

Authors Erik D. Demaine , Yael Kirkpatrick , Rebecca Lin

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LIPIcs.ITCS.2024.38.pdf
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  • Mathematics of computing → Graph algorithms
Keywords
  • Shortest walk
  • Eulerian cycle
  • perfect matching
  • beading

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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.

Cite As Get BibTex

Erik D. Demaine, Yael Kirkpatrick, and Rebecca Lin. Graph Threading. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 38:1-38:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ITCS.2024.38

Author Details

Erik D. Demaine
  • Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology, Cambridge, MA, USA
Yael Kirkpatrick
  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA
Rebecca Lin
  • Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology, Cambridge, MA, USA

Funding

  • Kirkpatrick, Yael: NSF Graduate Research Fellowship under Grant No. 2141064.
  • Lin, Rebecca: MIT Stata Family Presidential Fellowship.

Acknowledgements

We thank Anders Aamand, Kiril Bangachev, Justin Chen, Alison Martin, Surya Mathialagan, and Zhecheng Wang for insightful discussions. We also thank anonymous reviewers for their helpful comments.

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