Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Threshold dominating sets and an improved characterization of W[2]
Theoretical Computer Science
Reduction algorithms for graphs of small treewidth
Information and Computation
Vertex cover: further observations and further improvements
Journal of Algorithms
A new approach for approximating node deletion problems
Information Processing Letters
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Theoretical Computer Science - Parameterized and exact computation
Invitation to data reduction and problem kernelization
ACM SIGACT News
Solving NP-hard semirandom graph problems in polynomial expected time
Journal of Algorithms
Detecting Critical Regions in Covert Networks: A Case Study of 9/11 Terrorists Network
ARES '07 Proceedings of the The Second International Conference on Availability, Reliability and Security
Crown Structures for Vertex Cover Kernelization
Theory of Computing Systems
Crown reductions for the Minimum Weighted Vertex Cover problem
Discrete Applied Mathematics
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
The parameterized complexity of regular subgraph problems and generalizations
CATS '08 Proceedings of the fourteenth symposium on Computing: the Australasian theory - Volume 77
Algorithms and Experiments for Clique Relaxations--Finding Maximum s-Plexes
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
Isolation concepts for efficiently enumerating dense subgraphs
Theoretical Computer Science
Kernelization: New Upper and Lower Bound Techniques
Parameterized and Exact Computation
Fast fixed-parameter tractable algorithms for nontrivial generalizations of vertex cover
Discrete Applied Mathematics
An improved parameterized algorithm for a generalized matching problem
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses
Proceedings of the forty-second ACM symposium on Theory of computing
A linear kernel for co-path/cycle packing
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
An Extension of the Nemhauser-Trotter Theorem to Generalized Vertex Cover with Applications
SIAM Journal on Discrete Mathematics
Clique Relaxations in Social Network Analysis: The Maximum k-Plex Problem
Operations Research
A More Relaxed Model for Graph-Based Data Clustering: $s$-Plex Cluster Editing
SIAM Journal on Discrete Mathematics
Linear kernels in linear time, or how to save k colors in O(n2) steps
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Dinitz' algorithm: the original version and even's version
Theoretical Computer Science
On Bounded-Degree Vertex Deletion parameterized by treewidth
Discrete Applied Mathematics
Exact combinatorial algorithms and experiments for finding maximum k-plexes
Journal of Combinatorial Optimization
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The Nemhauser-Trotter local optimization theorem applies to the NP-hard Vertex Cover problem and has applications in approximation as well as parameterized algorithmics. We generalize Nemhauser and Trotter@?s result to vertex deletion problems, introducing a novel algorithmic strategy based on purely combinatorial arguments (not referring to linear programming as the Nemhauser-Trotter result originally did). The essence of our strategy can be understood as a doubly iterative process of cutting away ''easy parts'' of the input instance, finally leaving a ''hard core'' whose size is (almost) linearly related to the cardinality of the solution set. We exhibit our approach using a generalization of Vertex Cover, called Bounded-Degree Vertex Deletion. For some fixed d=0, Bounded-Degree Vertex Deletion asks to delete at most k vertices from a graph in order to transform it into a graph with maximum vertex degree at most d. Vertex Cover is the special case of d=0. Our generalization of the Nemhauser-Trotter-Theorem implies that Bounded-Degree Vertex Deletion, parameterized by k, admits an O(k)-vertex problem kernel for d=0, an O(k^1^+^@e)-vertex problem kernel for d=2. Finally, we provide a W[2]-completeness result for Bounded-Degree Vertex Deletion in case of unbounded d-values.