Abstract
We show that the minimal length-bounded \(L\)-cut can be computed in linear time with respect to \(L\) and the tree-width of the input graph as parameters. We derive an FPT algorithm for a more general multi-commodity length bounded cut problem when parameterized by the number of terminals also. For the former problem we show a \(\mathsf {W}[1]\)-hardness result when the parameterization is done by the path-width only (instead of the tree-width).
Research was supported by the project SVV-2014-260103.
Dušan Knop— Author supported by the project Kontakt LH12095, project GAUK 1784214 and project CE-ITI P202/12/G061.
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Acknowledgments
Authors thank to Jiří Fiala, Petr Kolman and Lukáš Folwarczný for fruitful discussions about the problem. We would like to mention that part of this research was done during Summer REU 2014 at Rutgers University.
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Dvořák, P., Knop, D. (2015). Parametrized Complexity of Length-Bounded Cuts and Multi-cuts. In: Jain, R., Jain, S., Stephan, F. (eds) Theory and Applications of Models of Computation. TAMC 2015. Lecture Notes in Computer Science(), vol 9076. Springer, Cham. https://doi.org/10.1007/978-3-319-17142-5_37
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