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On the Parameterized Complexity of Grid Contraction

Authors Saket Saurabh, Uéverton dos Santos Souza, Prafullkumar Tale

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Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
Keywords
  • Grid Contraction
  • FPT
  • Kernelization
  • Lower Bound

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Abstract

For a family of graphs 𝒢, the 𝒢-Contraction problem takes as an input a graph G and an integer k, and the goal is to decide if there exists F ⊆ E(G) of size at most k such that G/F belongs to 𝒢. Here, G/F is the graph obtained from G by contracting all the edges in F. In this article, we initiate the study of Grid Contraction from the parameterized complexity point of view. We present a fixed parameter tractable algorithm, running in time c^k ⋅ |V(G)|^{{O}(1)}, for this problem. We complement this result by proving that unless ETH fails, there is no algorithm for Grid Contraction with running time c^{o(k)} ⋅ |V(G)|^{{O}(1)}. We also present a polynomial kernel for this problem.

Cite As Get BibTex

Saket Saurabh, Uéverton dos Santos Souza, and Prafullkumar Tale. On the Parameterized Complexity of Grid Contraction. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 34:1-34:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.SWAT.2020.34

Author Details

Saket Saurabh
  • The Institute Of Mathematical Sciences, HBNI, Chennai, India
  • University of Bergen, Norway
Uéverton dos Santos Souza
  • Fluminense Federal Universidade, Niterói, Brazil
Prafullkumar Tale
  • Max Planck Institute for Informatics, Saarland Informatics Campus, Saarbrücken, Germany

Funding

  • Saurabh, Saket: This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 819416), and Swarnajayanti Fellowship (No DST/SJF/MSA01/2017-18).
  • Tale, Prafullkumar: This research is a part of a project that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement SYSTEMATICGRAPH (No. 725978).

Acknowledgements

Some part of this project was completed when the third author was a Senior Research Fellow at The Institute of Mathematical Sciences, HBNI, Chennai, India. The project started when the second and the third authors were visiting Prof. Michael Fellows at the University of Bergen, Bergen, Norway. Both the authors would like to thank Prof. Michael Fellows for the invitation.

References

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