On the Threshold of Intractability

  title={On the Threshold of Intractability},
  author={P{\aa}l Gr\on{\aa}s Drange and Markus S. Dregi and Daniel Lokshtanov and Blair D. Sullivan},
We study the computational complexity of the graph modification problems Threshold Editing and Chain Editing, adding and deleting as few edges as possible to transform the input into a threshold (or chain) graph. In this article, we show that both problems are NP-hard, resolving a conjecture by Natanzon, Shamir, and Sharan (Discrete Applied Mathematics, 113(1):109–128, 2001). On the positive side, we show the problem admits a quadratic vertex kernel. Furthermore, we give a subexponential time… CONTINUE READING
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