Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
A combinatorial algorithm minimizing submodular functions in strongly polynomial time
Journal of Combinatorial Theory Series B
A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
Constructive Linear Time Algorithms for Branchwidth
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Graphs of bounded rank-width
A Parametrized Algorithm for Matroid Branch-Width
SIAM Journal on Computing
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 fractional hypertree width
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Partitions versus sets: A case of duality
European Journal of Combinatorics
Approximating fractional hypertree width
ACM Transactions on Algorithms (TALG)
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
Tractable hypergraph properties for constraint satisfaction and conjunctive queries
Proceedings of the forty-second ACM symposium on Theory of computing
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
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)
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An integer-valued function f on the set 2^V of all subsets of a finite set V is a connectivity function if it satisfies the following conditions: (1) f(X)+f(Y)=f(X@?Y)+f(X@?Y) for all subsets X, Y of V, (2) f(X)=f(V@?X) for all X@?V, and (3) f(@A)=0. Branch-width is defined for graphs, matroids, and more generally, connectivity functions. We show that for each constant k, there is a polynomial-time (in |V|) algorithm to decide whether the branch-width of a connectivity function f is at most k, if f is given by an oracle. This algorithm can be applied to branch-width, carving-width, and rank-width of graphs. In particular, we can recognize matroids M of branch-width at most k in polynomial (in |E(M)|) time if the matroid is given by an independence oracle.