Arboricity and subgraph listing algorithms
SIAM Journal on Computing
On generating all maximal independent sets
Information Processing Letters
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Theoretical Computer Science
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Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
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Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
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COLT '97 Proceedings of the tenth annual conference on Computational learning theory
SIAM Journal on Computing
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Journal of the ACM (JACM)
Algorithms for k-colouring and finding maximal independent sets
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A Distributed Algorithm for finding All Maximal Cliques in a Network Graph
LATIN '92 Proceedings of the 1st Latin American Symposium on Theoretical Informatics
Finding All Maximal Cliques in Dynamic Graphs
Computational Optimization and Applications
Counting the number of independent sets in chordal graphs
Journal of Discrete Algorithms
On the complexity of monotone dualization and generating minimal hypergraph transversals
Discrete Applied Mathematics
Algorithms and theory of computation handbook
Linear-time counting algorithms for independent sets in chordal graphs
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Approximation scheme for lowest outdegree orientation and graph density measures
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Proceedings of the 7th International Conference on Ubiquitous Information Management and Communication
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We describe algorithms, based on Avis and Fukuda's reverse search paradigm, for listing all maximal independent sets in a sparse graph in polynomial time and delay per output. For bounded degree graphs, our algorithms take constant time per set generated; for minor-closed graph families, the time is O(n) per set, and for more general sparse graph families we achieve subquadratic time per set. We also describe new data structures for maintaining a dynamic vertex set S in a sparse or minor-closed graph family, and querying the number of vertices not dominated by S; for minor-closed graph families the time per update is constant, while it is sublinear for any sparse graph family. We can also maintain a dynamic vertex set in an arbitrary m-edge graph and test the independence of the maintained set in time O(√m) per update. We use the domination data structures as part of our enumeration algorithms.