Interval Completion Is Fixed Parameter Tractable

  title={Interval Completion Is Fixed Parameter Tractable},
  author={Yngve Villanger and P. Heggernes and C. Paul and J. Telle},
  journal={SIAM J. Comput.},
  • Yngve Villanger, P. Heggernes, +1 author J. Telle
  • Published 2009
  • Computer Science, Mathematics
  • SIAM J. Comput.
  • We present an algorithm with runtime $O(k^{2k}n^3m)$ for the following NP-complete problem [M. Garey and D. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman and Co., San Francisco, 1979, problem GT35]: Given an arbitrary graph $G$ on $n$ vertices and $m$ edges, can we obtain an interval graph by adding at most $k$ new edges to $G$? This resolves the long-standing open question [H. Kaplan, R. Shamir, and R. E. Tarjan, SIAM J. Comput., 28 (1999), pp… CONTINUE READING
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