Arboricity and subgraph listing algorithms
SIAM Journal on Computing
On generating all maximal independent sets
Information Processing Letters
Planar orientations with low out-degree and compaction of adjacency matrices
Theoretical Computer Science
A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Reverse search for enumeration
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
Generating all maximal independent sets of bounded-degree hypergraphs
COLT '97 Proceedings of the tenth annual conference on Computational learning theory
SIAM Journal on Computing
Smallest-last ordering and clustering and graph coloring algorithms
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
The worst-case time complexity for generating all maximal cliques and computational experiments
Theoretical Computer Science - Computing and combinatorics
Cliques in odd-minor-free graphs
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
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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(&sqrt;m) per update. We use the domination data structures as part of our enumeration algorithms.