# Exact and heuristic algorithms for Cograph Editing

@article{White2017ExactAH, title={Exact and heuristic algorithms for Cograph Editing}, author={W. Timothy J. White and Marcus Ludwig and Sebastian Bocker}, journal={arXiv: Data Structures and Algorithms}, year={2017} }

We present a dynamic programming algorithm for optimally solving the Cograph Editing problem on an $n$-vertex graph that runs in $O(3^n n)$ time and uses $O(2^n)$ space. In this problem, we are given a graph $G = (V, E)$ and the task is to find a smallest possible set $F \subseteq V \times V$ of vertex pairs such that $(V, E \bigtriangleup F)$ is a cograph (or $P_4$-free graph), where $\bigtriangleup$ represents the symmetric difference operator. We also describe a technique for speeding up the…

## 2 Citations

### Merging Modules is equivalent to Editing P4's

- MathematicsArt Discret. Appl. Math.
- 2020

It is shown here that editing the induced $P_4$s is equivalent to resolving prime modules by means of a suitable defined merge operation on the submodules.

### Cograph editing: merging modules is equivalent to editing P 4 S

- Mathematics
- 2020

Summary: The modular decomposition of a graph G = ( V, E ) does not contain prime modules if and only if G is a cograph, that is, if no quadruple of vertices induces a simple connected path P 4 . The…

## References

SHOWING 1-10 OF 13 REFERENCES

### Characterizing and computing minimal cograph completions

- Mathematics, Computer ScienceDiscret. Appl. Math.
- 2008

### Fixed-Parameter Tractability of Graph Modification Problems for Hereditary Properties

- MathematicsInf. Process. Lett.
- 1996

### Efficiency of a Good But Not Linear Set Union Algorithm

- MathematicsJACM
- 1975

It is shown that, if t(m, n) is seen as the maximum time reqmred by a sequence of m > n FINDs and n -- 1 intermixed UNIONs, then kima(m), n is shown to be related to a functional inverse of Ackermann's functmn and as very slow-growing.

### Phylogenomics with paralogs

- BiologyProceedings of the National Academy of Sciences
- 2015

It is demonstrated that the distribution of paralogs in large gene families contains in itself sufficient phylogenetic signal to infer fully resolved species phylogenies, and genome-wide data sets are sufficient to generate fully resolved phylogenetic trees, even in the presence of horizontal gene transfer.

### The complexity of some edge deletion problems

- Mathematics
- 1988

Previous complexity results are extended by showing that the EDP corresponding to any class H of graphs in each of the following cases is NP-hard.

### Complexity and parameterized algorithms for Cograph Editing

- Computer Science, MathematicsTheor. Comput. Sci.
- 2012