Improved bounds for matroid partition and intersection algorithms
SIAM Journal on Computing
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
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
The expression of graph properties and graph transformations in monadic second-order logic
Handbook of graph grammars and computing by graph transformation
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
Polynomial Time Recognition of Clique-Width \le \leq 3 Graphs (Extended Abstract)
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
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
log n-Approximative NLCk-Decomposition in O(n2k+1) Time
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
On the Relationship Between Clique-Width and Treewidth
SIAM Journal on Computing
A Parametrized Algorithm for Matroid Branch-Width
SIAM Journal on Computing
Matrices and Matroids for Systems Analysis
Matrices and Matroids for Systems Analysis
Parameterized Complexity
The recognizability of sets of graphs is a robust property
Theoretical Computer Science
Vertex disjoint paths on clique-width bounded graphs
Theoretical Computer Science
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
The relative clique-width of a graph
Journal of Combinatorial Theory Series B
On powers of graphs of bounded NLC-width (clique-width)
Discrete Applied Mathematics
Digraph measures: Kelly decompositions, games, and orderings
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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
Counting truth assignments of formulas of bounded tree-width or clique-width
Discrete Applied Mathematics
Digraph measures: Kelly decompositions, games, and orderings
Theoretical Computer Science
On Integer Programming and the Branch-Width of the Constraint Matrix
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Approximating rank-width and clique-width quickly
ACM Transactions on Algorithms (TALG)
Solving problems on recursively constructed graphs
ACM Computing Surveys (CSUR)
Clique-width: on the price of generality
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Approximating fractional hypertree width
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
The Rank-Width of the Square Grid
Graph-Theoretic Concepts in Computer Science
Graph operations characterizing rank-width
Discrete Applied Mathematics
Information Processing Letters
Recent developments on graphs of bounded clique-width
Discrete Applied Mathematics
Approximating fractional hypertree width
ACM Transactions on Algorithms (TALG)
On a disparity between relative cliquewidth and relative NLC-width
Discrete Applied Mathematics
The rank-width of the square grid
Discrete Applied Mathematics
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
Computing representations of matroids of bounded branch-width
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
Algorithms for propositional model counting
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Complexity and algorithms for well-structured k-SAT instances
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Tractable hypergraph properties for constraint satisfaction and conjunctive queries
Proceedings of the forty-second ACM symposium on Theory of computing
Rank-width and tree-width of H-minor-free graphs
European Journal of Combinatorics
Reasoning in Argumentation Frameworks of Bounded Clique-Width
Proceedings of the 2010 conference on Computational Models of Argument: Proceedings of COMMA 2010
Algorithmic lower bounds for problems parameterized by clique-width
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Decomposition width of matroids
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Compact labelings for efficient first-order model-checking
Journal of Combinatorial Optimization
New results on the complexity of the max- and min-rep problems
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Intractability of Clique-Width Parameterizations
SIAM Journal on Computing
Monadic second-order model-checking on decomposable matroids
Discrete Applied Mathematics
Fixed-point definability and polynomial time on chordal graphs and line graphs
Fields of logic and computation
Maximal matching and path matching counting in polynomial time for graphs of bounded clique width
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Linear-time algorithms for graphs of bounded rankwidt: a fresh look using game theory
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
F-rank-width of (edge-colored) graphs
CAI'11 Proceedings of the 4th international conference on Algebraic informatics
Computing graph polynomials on graphs of bounded clique-width
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Tree-representation of set families and applications to combinatorial decompositions
European Journal of Combinatorics
Exploiting restricted linear structure to cope with the hardness of clique-width
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Polynomial-time recognition of clique-width ≤3 graphs
Discrete Applied Mathematics
On the model-checking of monadic second-order formulas with edge set quantifications
Discrete Applied Mathematics
Decomposition width of matroids
Discrete Applied Mathematics
On parameterized approximability
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Solving #SAT using vertex covers
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Graph classes with structured neighborhoods and algorithmic applications
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
The complexity of finding uniform sparsest cuts in various graph classes
Journal of Discrete Algorithms
Tight complexity bounds for FPT subgraph problems parameterized by clique-width
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Journal of Graph Theory
Well-quasi-ordering of matrices under Schur complement and applications to directed graphs
European Journal of Combinatorics
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
First-Order and Monadic Second-Order Model-Checking on Ordered Structures
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Deciding first order properties of matroids
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Fixed-point definability and polynomial time on graphs with excluded minors
Journal of the ACM (JACM)
Abstract argumentation via monadic second order logic
SUM'12 Proceedings of the 6th international conference on Scalable Uncertainty Management
Feedback vertex set on graphs of low clique-width
European Journal of Combinatorics
A unified approach to polynomial algorithms on graphs of bounded (bi-)rank-width
European Journal of Combinatorics
Satisfiability of acyclic and almost acyclic CNF formulas
Theoretical Computer Science
A SAT approach to clique-width
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Cliquewidth and knowledge compilation
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Tractable Hypergraph Properties for Constraint Satisfaction and Conjunctive Queries
Journal of the ACM (JACM)
Clique-width and edge contraction
Information Processing Letters
Graph classes with structured neighborhoods and algorithmic applications
Theoretical Computer Science
Colouring of graphs with Ramsey-type forbidden subgraphs
Theoretical Computer Science
Obstructions for linear rank-width at most 1
Discrete Applied Mathematics
Digraphs of bounded elimination width
Discrete Applied Mathematics
Better Algorithms for Satisfiability Problems for Formulas of Bounded Rank-width
Fundamenta Informaticae - MFCS & CSL 2010 Satellite Workshops: Selected Papers
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We construct a polynomial-time algorithm to approximate the branch-width of certain symmetric sub-modular functions, and give two applications.The first is to graph "clique-width." Clique-width is a measure of the difficulty of decomposing a graph in a kind of tree-structure, and if a graph has clique-width at most k then the corresponding decomposition of the graph is called a "k-expression." We find (for fixed k) an O(n9 log n)-time algorithm that, with input an n-vertex graph, outputs either a (23k+2 - 1)-expression for the graph, or a witness that the graph has clique-width at least k + 1. (The best earlier algorithm, by Johansson [Ö. Johansson, log n-approximative NLCk-decomposition in O(n2k+1) time (extended abstract), in: Graph-Theoretic Concepts in Computer Science, Boltenhagen, 2001, in: Lecture Notes in Comput. Sci., vol. 2204, Springer, Berlin, 2001, pp. 229-240, constructs a 2k log n-expression for graphs of clique-width at most k.) It was already known that several graph problems, NP-hard on general graphs, are solvable in polynomial time if the input graph comes equipped with a k-expression (for fixed k). As a consequence of our algorithm, the same conclusion follows under the weaker hypothesis that the input graph has clique-width at most k (thus, we no longer need to be provided with an explicit k-expression).Another application is to the area of matroid branch-width. For fixed k, we find an O(n3.5)-time algorithm that, with input an n-element matroid in terms of its rank oracle, either outputs a branch-decomposition of width at most 3k - 1 or a witness that the matroid has branch-width at least k + 1. The previous algorithm by Hliněný [P. Hliněný, A parametrized algorithm for matroid branch-width, SIAM J. Comput. 35 (2) (2005) 259-277] works only for matroids represented over a finite field.