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Approximate Minimum Sum Colorings and Maximum k-Colorable Subgraphs of Chordal Graphs

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Algorithms and Data Structures (WADS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14079))

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Abstract

We give a \((1.796+\epsilon )\)-approximation for the minimum sum coloring problem on chordal graphs, improving over the previous 3.591-approximation by Gandhi et al. [2005]. To do so, we also design the first PTAS for the maximum k-colorable subgraph problem in chordal graphs.

I. DeHaan—Supported by an NSERC Undergraduate Student Research Award held at the University of Alberta.

Z. Friggstad—Supported by an NSERC Discovery Grant and Accelerator Supplement.

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Notes

  1. 1.

    We note [18] does have a similar calculation in a single-vehicle setting of their problem whose dependence is more like that in Lemma 6. They just don’t have a specific claim summarizing this calculation that we can reference.

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Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Canada

    Ian DeHaan

  2. Department of Computing Science, University of Alberta, Edmonton, Canada

    Zachary Friggstad

Authors
  1. Ian DeHaan
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  2. Zachary Friggstad
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Correspondence to Ian DeHaan .

Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, ON, Canada

    Pat Morin

  2. University of California, Santa Barbara, CA, USA

    Subhash Suri

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DeHaan, I., Friggstad, Z. (2023). Approximate Minimum Sum Colorings and Maximum k-Colorable Subgraphs of Chordal Graphs. In: Morin, P., Suri, S. (eds) Algorithms and Data Structures. WADS 2023. Lecture Notes in Computer Science, vol 14079. Springer, Cham. https://doi.org/10.1007/978-3-031-38906-1_22

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  • DOI: https://doi.org/10.1007/978-3-031-38906-1_22

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  • Online ISBN: 978-3-031-38906-1

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