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Parameterized Algorithms for Linear Layouts of Graphs with Respect to the Vertex Cover Number

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Combinatorial Optimization and Applications (COCOA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13135))

Abstract

The linear layout of graphs problem asks, given a graph G = (V, E) and an integer k, whether G admits a linear layout consisting of a linear order of V and a partition of E into k sets such that the edges in each set satisfy some restrictions. In this paper, we study parameterized algorithms for a series of specific linear layout problems with respect to the vertex cover number \(\tau \) of the input graph. We first focus on the mixed s -stack q -queue layout problem and show that it admits a kernel of size \(2^{\mathcal O(\tau )}\) and an algorithm running in time \(\mathcal O(2^{2^{\mathcal O(\tau )}}+\tau \cdot |V|)\), where |V| denotes the size of the input graph. Our work does not only confirm the existence of a fixed-parameter tractable algorithm for this problem which was mentioned by Bhore et al. (GD 2020), but also derives new results improving that for the k -stack layout problem (J. Graph Alg. Appl. 2020), that for the upward k -stack layout problem (GD 2021), and that for the k -queue layout problem (GD 2020) respectively. We also generalize our techniques to the k -arch layout problem and obtain a similar result.

This research was supported in part by the National Natural Science Foundation of China under Grant No. 61572190 and Hunan Provincial Science and Technology Program under Grant No. 2018TP1018.

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Acknowledgements

The authors thank the anonymous referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. College of Information Science and Engineering, Hunan Provincial Key Laboratory of Intelligent Computing and Language Information Processing, Hunan Normal University, Changsha, 410081, People’s Republic of China

    Yunlong Liu, Yixuan Li & Jingui Huang

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  1. Yunlong Liu
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  2. Yixuan Li
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  3. Jingui Huang
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Correspondence to Yunlong Liu or Jingui Huang .

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Editors and Affiliations

  1. University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  2. University of New Brunswick, Fredericton, NB, Canada

    Donglei Du

  3. Tianjin University of Technology, Tianjin, China

    Chenchen Wu

  4. Beijing University of Technology, Beijing, China

    Dachuan Xu

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Liu, Y., Li, Y., Huang, J. (2021). Parameterized Algorithms for Linear Layouts of Graphs with Respect to the Vertex Cover Number. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Combinatorial Optimization and Applications. COCOA 2021. Lecture Notes in Computer Science(), vol 13135. Springer, Cham. https://doi.org/10.1007/978-3-030-92681-6_43

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  • DOI: https://doi.org/10.1007/978-3-030-92681-6_43

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  • Print ISBN: 978-3-030-92680-9

  • Online ISBN: 978-3-030-92681-6

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