A general method to speed up fixed-parameter-tractable algorithms
Information Processing Letters
The Maximum k-Dependent and f-Dependent Set Problem
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
A fast algorithm for the maximum clique problem
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Invitation to data reduction and problem kernelization
ACM SIGACT News
Crown Structures for Vertex Cover Kernelization
Theory of Computing Systems
Iterative Compression for Exactly Solving NP-Hard Minimization Problems
Algorithmics of Large and Complex Networks
Isolation concepts for efficiently enumerating dense subgraphs
Theoretical Computer Science
Enumeration of isolated cliques and pseudo-cliques
ACM Transactions on Algorithms (TALG)
Isolation concepts for clique enumeration: Comparison and computational experiments
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
Fixed-Parameter Algorithms for Cluster Vertex Deletion
Theory of Computing Systems - Special Section: Algorithmic Game Theory; Guest Editors: Burkhard Monien and Ulf-Peter Schroeder
A parallel algorithm for enumerating all the maximal k-plexes
PAKDD'07 Proceedings of the 2007 international conference on Emerging technologies in knowledge discovery and data mining
A linear kernel for co-path/cycle packing
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
Clique Relaxations in Social Network Analysis: The Maximum k-Plex Problem
Operations Research
A generalization of Nemhauser and Trotter's local optimization theorem
Journal of Computer and System Sciences
A More Relaxed Model for Graph-Based Data Clustering: $s$-Plex Cluster Editing
SIAM Journal on Discrete Mathematics
Combinatorial algorithms for the maximum k-plex problem
Journal of Combinatorial Optimization
Parameterized Complexity
Computational Optimization and Applications
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We propose new practical algorithms to find maximum-cardinality k-plexes in graphs. A k-plex denotes a vertex subset in a graph inducing a subgraph where every vertex has edges to all but at most k vertices in the k-plex. Cliques are 1-plexes. In analogy to the special case of finding maximum-cardinality cliques, finding maximum-cardinality k-plexes is NP-hard. Complementing previous work, we develop exact combinatorial algorithms, which are strongly based on methods from parameterized algorithmics. The experiments with our freely available implementation indicate the competitiveness of our approach, for many real-world graphs outperforming the previously used methods.