The Tutte Polynomial for Matroids of Bounded Branch-Width
Combinatorics, Probability and Computing
Trees, grids, and MSO decidability: from graphs to matroids
Theoretical Computer Science - Parameterized and exact computation
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
Branch-width, parse trees, and monadic second-order logic for matroids
Journal of Combinatorial Theory Series B
European Journal of Combinatorics - Special issue on Eurocomb'03 - graphs and combinatorial structures
Journal of Combinatorial Theory Series B
Approximating rank-width and clique-width quickly
ACM Transactions on Algorithms (TALG)
On minimal tree realizations of linear codes
IEEE Transactions on Information Theory
Computing representations of matroids of bounded branch-width
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Finding branch-decompositions and rank-decompositions
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Decomposition width of matroids
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Decomposition width of matroids
Discrete Applied Mathematics
Deciding first order properties of matroids
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Computability of width of submodular partition functions
European Journal of Combinatorics
Tractable Hypergraph Properties for Constraint Satisfaction and Conjunctive Queries
Journal of the ACM (JACM)
Better Algorithms for Satisfiability Problems for Formulas of Bounded Rank-width
Fundamenta Informaticae - MFCS & CSL 2010 Satellite Workshops: Selected Papers
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Branch-width is a structural parameter very closely related to tree-width, but branch-width has an immediate generalization from graphs to matroids. We present an algorithm that, for a given matroid M of bounded branch-width t which is represented over a finite field, finds a branch decomposition of M of width at most 3t in cubic time. Then we show that the branch-width of M is a uniformly fixed-parameter tractable problem. Other applications include recognition of matroid properties definable in the monadic second-order logic for bounded branch-width, and [S.-I. Oum, Approximating rank-width and clique-width quickly, in Proceedings of the 31st International Workshop on Graph-Theoretic Concepts in Computer Science, Springer-Verlag, Heidelberg, to appear] a cubic time approximation algorithm for graph rank-width and clique-width.