Complexity and Exact Algorithms for Mulitcut

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Introduction RVMC in Trees RVMC in Interval Graphs RVMC in General Graphs ConclusionHardness results for general graphsRestricted Vertex Multicut is NP-complete if thereare at least six terminals. [Dahlhaus et al., SIAM Journal onComputing, 1994]There is no FPT-algorithm with respect to the parameter“number of terminals”.RVMC is NP-complete for trees with bounded vertex degreeand bounded pathwidth → no FPT-algorithm with path- ortreewidth as parameter.IdeaA combination of both parameters “number of terminals” andtreewidth leads to an FPT-algorithm.
Introduction RVMC in Trees RVMC in Interval Graphs RVMC in General Graphs ConclusionFPT-algorithm — basic ideaKey observation: Any solution of RVMC divides the input graphinto at least two connected components → the two terminals of aterminal pair are in distinct connected components!
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Complexity and Exact Algorithms for Mulitcut

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