Journal of Algorithms
Fixed-parameter tractability of graph modification problems for hereditary properties
Information Processing Letters
Characterizations and algorithmic applications of chordal graph embeddings
Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
The homogeneous set sandwich problem
Information Processing Letters
Theoretical Computer Science
Treewidth and Minimum Fill-in: Grouping the Minimal Separators
SIAM Journal on Computing
A Polynomial Approximation Algorithm for the Minimum Fill-In Problem
SIAM Journal on Computing
The graph sandwich problem for 1-join composition is NP-complete
Discrete Applied Mathematics
Two Strikes Against Perfect Phylogeny
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Computing minimal triangulations in time O(nα log n) = o(n2.376)
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
On the complexity of the sandwich problems for strongly chordal graphs and chordal bipartite graphs
Theoretical Computer Science
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Exact Algorithms for Treewidth and Minimum Fill-In
SIAM Journal on Computing
On Problems without Polynomial Kernels (Extended Abstract)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Faster Parameterized Algorithms for Minimum Fill-In
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Chordal Deletion is Fixed-Parameter Tractable
Algorithmica
On the complexity of computing treelength
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Reducing problems in unrooted tree compatibility to restricted triangulations of intersection graphs
WABI'12 Proceedings of the 12th international conference on Algorithms in Bioinformatics
TREEWIDTH and PATHWIDTH parameterized by the vertex cover number
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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Given an arbitrary graph G=(V,E) and an additional set of admissible edges F, the Chordal Sandwich problem asks whether there exists a chordal graph (V,E∪F′) such that F′⊆F. This problem arises from perfect phylogeny in evolution and from sparse matrix computations in numerical analysis, and it generalizes the widely studied problems of completions and deletions of arbitrary graphs into chordal graphs. As many related problems, Chordal Sandwich is NP-complete. In this paper we show that the problem becomes tractable when parameterized with a suitable natural measure on the set of admissible edges F. In particular, we give an algorithm with running time $\mathcal{O}(2^{k}n^{5})$ to solve this problem, where k is the size of a minimum vertex cover of the graph (V, F). Hence we show that the problem is fixed parameter tractable when parameterized by k. Note that the parameter does not assume any restriction on the input graph, and it concerns only the additional edge set F.