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Hardness of Approximation for H-Free Edge Modification Problems: Towards a Dichotomy

Authors Tatiana Belova, Ivan Bliznets



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Tatiana Belova
  • St. Petersburg Department of Steklov Mathematical Institute of the RAS, Russia
Ivan Bliznets
  • St. Petersburg Department of Steklov Mathematical Institute of the RAS, Russia

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Tatiana Belova and Ivan Bliznets. Hardness of Approximation for H-Free Edge Modification Problems: Towards a Dichotomy. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 24:1-24:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ISAAC.2022.24

Abstract

For a fixed graph H, the H-free Edge Deletion/Completion/Editing problem asks to delete/add/edit the minimum possible number of edges in G to get a graph that does not contain an induced subgraph isomorphic to the graph H. In this work, we investigate H-free Edge Deletion/Completion/Editing problems in terms of the hardness of their approximation. We formulate a conjecture according to which all the graphs with at least five vertices can be classified into several groups of graphs with specific structural properties depending on the hardness of approximation for the corresponding H-free Edge Deletion/Completion/Editing problems. Also, we make significant progress in proving that conjecture by showing that it is sufficient to resolve it only for a finite set of graphs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
Keywords
  • Parameterized complexity
  • Hardness of approximation
  • Edge modification problems

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