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Sampling List Packings

Authors Evan Camrud , Ewan Davies , Alex Karduna, Holden Lee

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Author Details

Evan Camrud
  • Department of Mathematics and Statistics, Middlebury College, VT, USA
Ewan Davies
  • Department of Computer Science, Colorado State University, Fort Collins, CO, USA
Alex Karduna
  • Department of Computer Science, Colorado State University, Fort Collins, CO, USA
Holden Lee
  • Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, USA

Funding

  • Davies, Ewan: supported in part by NSF grant CCF-2309707.

Acknowledgements

We thank Colin McSwiggen and Semon Rezchikov for organizing Random Theory 2023, where this collaboration began. We thank Charlie Carlson and Guillem Perarnau for comments that led to improvements to the exposition of the paper.

Cite As Get BibTex

Evan Camrud, Ewan Davies, Alex Karduna, and Holden Lee. Sampling List Packings. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.24

Abstract

We initiate the study of approximately counting the number of list packings of a graph. The analogous problem for usual vertex coloring and list coloring has attracted substantial attention. For list packing the setup is similar, but we seek a full decomposition of the lists of colors into pairwise-disjoint proper list colorings. The existence of a list packing implies the existence of a list coloring, but the converse is false. Recent works on list packing have focused on existence or extremal results of on the number of list packings, but here we turn to the algorithmic aspects of counting and sampling. 
In graphs of maximum degree Δ and when the number of colors is at least Ω(Δ²), we give a fully polynomial-time randomized approximation scheme (FPRAS) based on rapid mixing of a natural Markov chain (the Glauber dynamics) which we analyze with the path coupling technique. Some motivation for our work is the investigation of an atypical spin system, one where the number of spins for each vertex is much larger than the graph degree.

Subject Classification

ACM Subject Classification
  • Theory of computation → Random walks and Markov chains
  • Mathematics of computing → Approximation algorithms
Keywords
  • List packing
  • Graph colouring
  • Markov chains
  • Path coupling

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References

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