Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
k-NLC graphs and polynomial algorithms
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
Edge dominating set and colorings on graphs with fixed clique-width
Discrete Applied Mathematics
How to Solve NP-hard Graph Problems on Clique-Width Bounded Graphs in Polynomial Time
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Algorithms for vertex-partitioning problems on graphs with fixed clique-width
Theoretical Computer Science
Journal of Combinatorial Theory Series B
Branch-width, parse trees, and monadic second-order logic for matroids
Journal of Combinatorial Theory Series B
Vertex-minors, monadic second-order logic, and a conjecture by Seese
Journal of Combinatorial Theory Series B
MSOL partitioning problems on graphs of bounded treewidth and clique-width
Theoretical Computer Science
Vertex-minor reductions can simulate edge contractions
Discrete Applied Mathematics
Hypertree width and related hypergraph invariants
European Journal of Combinatorics
Polynomial algorithms for protein similarity search for restricted mRNA structures
Information Processing Letters
Solving problems on recursively constructed graphs
ACM Computing Surveys (CSUR)
Approximating fractional hypertree width
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Connection Matrices for MSOL-Definable Structural Invariants
ICLA '09 Proceedings of the 3rd Indian Conference on Logic and Its Applications
Linear delay enumeration and monadic second-order logic
Discrete Applied Mathematics
Approximating fractional hypertree width
ACM Transactions on Algorithms (TALG)
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Graph operations characterizing rank-width and balanced graph expressions
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Finding branch-decompositions and rank-decompositions
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Tractable hypergraph properties for constraint satisfaction and conjunctive queries
Proceedings of the forty-second ACM symposium on Theory of computing
Algorithms and theory of computation handbook
The enumeration of vertex induced subgraphs with respect to the number of components
European Journal of Combinatorics
From a zoo to a zoology: descriptive complexity for graph polynomials
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Computing the tutte polynomial on graphs of bounded clique-width
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
On parameterized approximability
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Resources required for preparing graph states
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Tractable Hypergraph Properties for Constraint Satisfaction and Conjunctive Queries
Journal of the ACM (JACM)
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Rank-width is defined by Seymour and the author to investigate clique-width; they show that graphs have bounded rank-width if and only if they have bounded clique-width. It is known that many hard graph problems have polynomial-time algorithms for graphs of bounded clique-width, however, requiring a given decomposition corresponding to clique-width (k-expression); they remove this requirement by constructing an algorithm that either outputs a rank-decomposition of width at most f(k) for some function f or confirms rank-width is larger than k in O(|V|9log |V|) time for an input graph G = (V,E) and a fixed k. This can be reformulated in terms of clique-width as an algorithm that either outputs a (21+f(k)–1)-expression or confirms clique-width is larger than k in O(|V|9log |V|) time for fixed k. In this paper, we develop two separate algorithms of this kind with faster running time. We construct a O(|V|4)-time algorithm with f(k) = 3k + 1 by constructing a subroutine for the previous algorithm; we may now avoid using general submodular function minimization algorithms used by Seymour and the author. Another one is a O(|V|3)-time algorithm with f(k) = 24k by giving a reduction from graphs to binary matroids; then we use an approximation algorithm for matroid branch-width by Hliněný.