Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Measure and conquer: a simple O(20.288n) independent set algorithm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Fast fixed-parameter tractable algorithms for nontrivial generalizations of vertex cover
Discrete Applied Mathematics
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized enumeration, transversals, and imperfect phylogeny reconstruction
Theoretical Computer Science - Parameterized and exact computation
The worst-case time complexity for generating all maximal cliques and computational experiments
Theoretical Computer Science - Computing and combinatorics
Enumeration of isolated cliques and pseudo-cliques
ACM Transactions on Algorithms (TALG)
Clique Relaxations in Social Network Analysis: The Maximum k-Plex Problem
Operations Research
Isolation concepts for enumerating dense subgraphs
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Cliques with maximum/minimum edge neighborhood and neighborhood density
Computers and Operations Research
A generalization of Nemhauser and Trotter's local optimization theorem
Journal of Computer and System Sciences
On Bounded-Degree Vertex Deletion parameterized by treewidth
Discrete Applied Mathematics
A More Relaxed Model for Graph-Based Data Clustering: $s$-Plex Cluster Editing
SIAM Journal on Discrete Mathematics
Exact combinatorial algorithms and experiments for finding maximum k-plexes
Journal of Combinatorial Optimization
A separability framework for analyzing community structure
ACM Transactions on Knowledge Discovery from Data (TKDD) - Casin special issue
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In an undirected graph G=(V,E), a set of k vertices is called c-isolated if it has less than c@?k outgoing edges. Ito and Iwama [H. Ito, K. Iwama, Enumeration of isolated cliques and pseudo-cliques, ACM Transactions on Algorithms (2008) (in press)] gave an algorithm to enumerate all c-isolated maximal cliques in O(4^c@?c^4@?|E|) time. We extend this to enumerating all maximal c-isolated cliques (which are a superset) and improve the running time bound to O(2.89^c@?c^2@?|E|), using modifications which also facilitate parallelizing the enumeration. Moreover, we introduce a more restricted and a more general isolation concept and show that both lead to faster enumeration algorithms. Finally, we extend our considerations to s-plexes (a relaxation of the clique notion), providing a W[1]-hardness result when the size of the s-plex is the parameter and a fixed-parameter algorithm for enumerating isolated s-plexes when the parameter describes the degree of isolation.