A survey of graph layout problems
ACM Computing Surveys (CSUR)
Linear-time recognition of bipartite graphs plus two edges
Discrete Mathematics
Fast Fixed-Parameter Tractable Algorithms for Nontrivial Generalizations of Vertex Cover
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Parameterized complexity of vertex colouring
Discrete Applied Mathematics
Fast fixed-parameter tractable algorithms for nontrivial generalizations of vertex cover
Discrete Applied Mathematics
Parameterized coloring problems on chordal graphs
Theoretical Computer Science - Parameterized and exact computation
On the interval completion of chordal graphs
Discrete Applied Mathematics
Interval completion with few edges
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Minimal proper interval completions
Information Processing Letters
Random Generation and Enumeration of Proper Interval Graphs
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Dynamically maintaining split graphs
Discrete Applied Mathematics
Strongly Chordal and Chordal Bipartite Graphs Are Sandwich Monotone
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Fast fixed-parameter tractable algorithms for nontrivial generalizations of vertex cover
Discrete Applied Mathematics
On the interval completion of chordal graphs
Discrete Applied Mathematics
Minimum fill-in and treewidth of split+ke and split+kv graphs
Discrete Applied Mathematics
Graph-modeled data clustering: fixed-parameter algorithms for clique generation
CIAC'03 Proceedings of the 5th Italian conference on Algorithms and complexity
Characterizing minimal interval completions towards better understanding of profile and pathwidth
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
A clustering algorithm for interval graph test on noisy data
WEA'03 Proceedings of the 2nd international conference on Experimental and efficient algorithms
Minimum fill-in and treewidth of split+ke and split+kv graphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Wheel-free deletion is W[2]-hard
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
A novel branching strategy for parameterized graph modification problems
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
On the Compressibility of $\mathcal{NP}$ Instances and Cryptographic Applications
SIAM Journal on Computing
Strongly chordal and chordal bipartite graphs are sandwich monotone
Journal of Combinatorial Optimization
Chordal deletion is fixed-parameter tractable
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Minimal proper interval completions
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Subexponential parameterized algorithm for minimum fill-in
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Fast FPT-Algorithms for cleaning grids
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Error compensation in leaf root problems
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
A parameterized algorithm for chordal sandwich
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Planar disjoint-paths completion
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
What's next? future directions in parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
A faster FPT algorithm for Bipartite Contraction
Information Processing Letters
Polynomial kernels for Proper Interval Completion and related problems
Information and Computation
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We study the parameterized complexity of three NP-hard graph completion problems.The minimum fill-in problem asks if a graph can be triangulated by adding at most k edges. We develop O(ck m) and O(k2mn+f(k)) algorithms for this problem on a graph with n vertices and m edges. Here f(k) is exponential in k and the constants hidden by the big-O notation are small and do not depend on k. In particular, this implies that the problem is fixed-parameter tractable (FPT).The proper interval graph completion problem, motivated by molecular biology, asks if a graph can be made proper interval by adding no more than k edges. We show that the problem is FPT by providing a simple search-tree-based algorithm that solves it in O(ck m)-time. Similarly, we show that the parameterized version of the strongly chordal graph completion problem is FPT by giving an O(ck m log n)-time algorithm for it.All of our algorithms can actually enumerate all possible k-completions within the same time bounds.