A Subexponential Parameterized Algorithm for Proper Interval Completion

@inproceedings{Bliznets2014ASP,
  title={A Subexponential Parameterized Algorithm for Proper Interval Completion},
  author={Ivan A. Bliznets and F. Fomin and Marcin Pilipczuk and Michal Pilipczuk},
  booktitle={Embedded Systems and Applications},
  year={2014}
}
In the Proper Interval Completion problem we are given a graph G and an integer k, and the task is to turn G using at most k edge additions into a proper interval graph, i.e., a graph admitting an intersection model of equal-length intervals on a line. The study of Proper Interval Completion from the viewpoint of parameterized complexity has been initiated by Kaplan, Shamir and Tarjan [FOCS 1994; SIAM J. Comput. 1999], who showed an algorithm for the problem working in \(\mathcal{O}(16^k\cdot… 
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26 Citations
Background Citations
13
Methods Citations
5

26 Citations

Subexponential Parameterized Algorithm for Interval Completion

The first subexponential parameterized algorithm solving Interval Completion in time kO(√k)nO(1) is given, adding IntervalCompletion to a very small list of parameterized graph modification problems solvable in subexp exponential time.

Lower Bounds for the Parameterized Complexity of Minimum Fill-in and Other Completion Problems

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Exploring Subexponential Parameterized Complexity of Completion Problems

It is proved that completions into several well studied classes of graphs without long induced cycles also admit parameterized subexponential time algorithms.

On the proper interval completion problem within some chordal subclasses

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Paths to Trees and Cacti

The goal of designing polynomial kernels for trees with bounded number of leaves is considered and kernelization lower bounds are given for Bounded TC, Bounded OTC and Bounded CC by showing that unless NP coNP/poly the size of the kernel the authors obtain is optimal.

Parameterized Graph Modification Algorithms

This thesis shows that editing towards trivially perfect graphs, threshold graphs, and chain graphs are all NP-complete, resolving 15 year old open questions and provides several new results in classical complexity, kernelization complexity, and subexponential parameterized complexity.

On the Parameterized Approximability of Contraction to Classes of Chordal Graphs

This paper studies the problem of parameterized approximation of editing to a family of graphs by contracting edges by observing that the existing \textsf{W[2]-hardness} reduction can be adapted to show that there is no $F(k)$-\FPT-approximation algorithm for \textsc{Chordal Contraction}.

Unit interval editing is fixed-parameter tractable

  • Yixin Cao
  • Computer Science, Mathematics
    Inf. Comput.
  • 2015

Rank Reduction of Directed Graphs by Vertex and Edge Deletions

The main structural result, which is the fulcrum of all the algorithmic results, is that for a fixed integer r the size of any “reduced graph” in \(\mathcal{F}_r\) is upper bounded by \(3^r\).

FPT Algorithms for Plane Completion Problems

FPT algorithms that solve both problems in f (|E(∆)|) · |E(Γ)| 2 steps are given and it is shown that f(k)=2^{O(k*log(k))}.

References

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The first subexponential parameterized algorithm solving Interval Completion in time kO(√k)nO(1) is given, adding IntervalCompletion to a very small list of parameterized graph modification problems solvable in subexp exponential time.

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