The Complexity of Physical Mapping with Strict Chimerism
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
Complexity Classification of Some Edge Modification Problems
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Characterizing and Computing Minimal Cograph Completions
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
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
Characterizing and computing minimal cograph completions
Discrete Applied Mathematics
Minimum fill-in and treewidth of split+ke and split+kv graphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Polynomial kernels for proper interval completion and related problems
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Subexponential parameterized algorithm for minimum fill-in
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A parameterized algorithm for chordal sandwich
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
W[2]-hardness of precedence constrained K-processor scheduling
Operations Research Letters
The birth and early years of parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
A basic parameterized complexity primer
The Multivariate Algorithmic Revolution and Beyond
Polynomial kernels for Proper Interval Completion and related problems
Information and Computation
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We study the parameterized complexity of several NP-Hard graph completion problems: The minimum fill-in problem is to decide if a graph can be triangulated by adding at most k edges. We develop an O(k/sup 5/ mn+f(K)) algorithm for the problem on a graph with n vertices and m edges. In particular, this implies that the problem is fixed parameter tractable (FPT). proper interval graph completion problems, motivated by molecular biology, ask for adding edges in order to obtain a proper interval graph, so that a parameter in that graph does not exceed k. We show that the problem is FPT when k is the number of added edges. For the problem where k is the clique size, we give an O(f(k)n/sup k-1/) algorithm, so it is polynomial for fixed k. On the other hand, we prove its hardness in the parameterized hierarchy, so it is probably not FPT. Those results are obtained even when a set of edges which should not be added is given. That set can be given either explicitly or by a proper vertex coloring which the added edges should respect.