Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.  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,  introduce a more restricted and a more general isolation concept and show that both lead to faster enumeration algorithms. Finally,  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.
['Christian Komusiewicz', 'Falk Hüffner', 'Hannes Moser', 'Rolf Niedermeier']
I am writing a research paper on a idea Isolation concepts for efficiently enumerating dense subgraphs
[{"from": "human", "value": "I am writing a research paper on a idea Isolation concepts for efficiently enumerating dense subgraphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.  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,  introduce a more restricted and a more general isolation concept and show that both lead to faster enumeration algorithms. Finally,  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."}]