Easy problems for tree-decomposable graphs
Journal of Algorithms
Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
Multicuts in unweighted graphs and digraphs with bounded degree and bounded tree-width
Journal of Algorithms
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized graph separation problems
Theoretical Computer Science - Parameterized and exact computation
Complexity and exact algorithms for multicut
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
Parameterized Complexity
Size and treewidth bounds for conjunctive queries
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Proceedings of the forty-third annual ACM symposium on Theory of computing
Fixed-parameter tractability of multicut parameterized by the size of the cutset
Proceedings of the forty-third annual ACM symposium on Theory of computing
Multicut algorithms via tree decompositions
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Size and Treewidth Bounds for Conjunctive Queries
Journal of the ACM (JACM)
On the parameterized complexity of finding separators with non-hereditary properties
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Finding small separators in linear time via treewidth reduction
ACM Transactions on Algorithms (TALG)
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Multicut problems are well-studied NP-complete problems in the field of network theory. Previously, by using graph theoretic methods, they have been shown to be fixed parameter tractable for different combinations of parameters, but not for any single parameter. In this paper different versions of the multicut problem are expressed in Monadic Second Order Logic (MSO) and an extended version of Courcelle's Theorem due to Arnborg, Lagergren and Seese is used to demonstrate that these problems are fixed parameter tractable with respect to the parameter @w^*, the treewidth of the input structure. Here, the input structure consists of a set V of vertices with two relations, the edge relation E of the input graph G=(V,E), and a relation H encoding all pairs of vertices to be disconnected. The contribution of this paper is two-fold: to introduce a single parameter for which the major variants of the multicut problem are fixed parameter tractable, and to use multicut problems as examples for demonstrating fruitful practical applications of logical properties and results in network theory.