Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Randomized algorithms
Algorithms for Vertex Partitioning Problems on Partial k-Trees
SIAM Journal on Discrete Mathematics
Edge dominating set and colorings on graphs with fixed clique-width
Discrete Applied Mathematics
Algorithms for vertex-partitioning problems on graphs with fixed clique-width
Theoretical Computer Science
On the Relationship Between Clique-Width and Treewidth
SIAM Journal on Computing
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Dynamic programming and fast matrix multiplication
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Vertex-minor reductions can simulate edge contractions
Discrete Applied Mathematics
Rank-width is less than or equal to branch-width
Journal of Graph Theory
Parameterized and Exact Computation
On parse trees and Myhill-Nerode-type tools for handling graphs of bounded rank-width
Discrete Applied Mathematics
H-join decomposable graphs and algorithms with runtime single exponential in rankwidth
Discrete Applied Mathematics
Width Parameters Beyond Tree-width and their Applications
The Computer Journal
Parameterized complexity of generalized domination problems
Discrete Applied Mathematics
Graph classes with structured neighborhoods and algorithmic applications
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Finding good decompositions for dynamic programming on dense graphs
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Fast dynamic programming for locally checkable vertex subset and vertex partitioning problems
Theoretical Computer Science
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Boolean-width is a recently introduced graph invariant. Similar to tree-width, it measures the structural complexity of graphs. Given any graph G and a decomposition of G of boolean-width k, we give algorithms solving a large class of vertex subset and vertex partitioning problems in time O*(2O(k2)). We relate the boolean-width of a graph to its branch-width and to the boolean-width of its incidence graph. For this we use a constructive proof method that also allows much simpler proofs of similar results on rank-width in [S. Oum. Rank-width is less than or equal to branch-width. Journal of Graph Theory 57(3):239-244, 2008]. For an n-vertex random graph, with a uniform edge distribution, we show that almost surely its boolean-width is Θ(log2 n) - setting boolean-width apart from other graph invariants - and it is easy to find a decomposition witnessing this. Combining our results gives algorithms that on input a random graph on n vertices will solve a large class of vertex subset and vertex partitioning problems in quasi-polynomial time O*(2O(log4 n)).