Improved Kernels for Edge Modification Problems

Authors Yixin Cao , Yuping Ke

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Yixin Cao
  • Department of Computing, Hong Kong Polytechnic University, Hong Kong, China
Yuping Ke
  • Department of Computing, Hong Kong Polytechnic University, Hong Kong, China

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Yixin Cao and Yuping Ke. Improved Kernels for Edge Modification Problems. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 13:1-13:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


In an edge modification problem, we are asked to modify at most k edges of a given graph to make the graph satisfy a certain property. Depending on the operations allowed, we have the completion problems and the edge deletion problems. A great amount of efforts have been devoted to understanding the kernelization complexity of these problems. We revisit several well-studied edge modification problems, and develop improved kernels for them: - a 2 k-vertex kernel for the cluster edge deletion problem, - a 3 k²-vertex kernel for the trivially perfect completion problem, - a 5 k^{1.5}-vertex kernel for the split completion problem and the split edge deletion problem, and - a 5 k^{1.5}-vertex kernel for the pseudo-split completion problem and the pseudo-split edge deletion problem. Moreover, our kernels for split completion and pseudo-split completion have only O(k^{2.5}) edges. Our results also include a 2 k-vertex kernel for the strong triadic closure problem, which is related to cluster edge deletion.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Kernelization
  • edge modification
  • cluster
  • trivially perfect graphs
  • split graphs


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