Parameterized Complexity of Length-bounded Cuts and Multicuts

@article{Dvok2018ParameterizedCO,
  title={Parameterized Complexity of Length-bounded Cuts and Multicuts},
  author={P. Dvoř{\'a}k and D. Knop},
  journal={Algorithmica},
  year={2018},
  volume={80},
  pages={3597-3617}
}
  • P. Dvořák, D. Knop
  • Published 2018
  • Mathematics, Computer Science
  • Algorithmica
  • We study the Minimum Length-Bounded Cut problem where the task is to find a set of edges of a graph such that after removal of this set, the shortest path between two prescribed vertices is at least $$L + 1$$L+1 long. We show the problem can be computed in $$\mathsf {FPT}$$FPT time with respect to L and the tree-width of the input graph G as parameters and with linear dependence of |V(G)| (i.e., in time $$f (L, {\text {tw}}(G))|V(G)|$$f(L,tw(G))|V(G)| for a computable function f). We derive an… CONTINUE READING
    7 Citations
    Length-Bounded Cuts: Proper Interval Graphs and Structural Parameters
    • 2
    • Highly Influenced
    • PDF
    Improved Hardness for Cut, Interdiction, and Firefighter Problems
    • 23
    • PDF
    Grundy Distinguishes Treewidth from Pathwidth
    • 2
    • PDF
    A survey of parameterized algorithms and the complexity of edge modification
    • 9
    • PDF
    As Time Goes By: Reflections on Treewidth for Temporal Graphs
    • PDF

    References

    SHOWING 1-10 OF 34 REFERENCES
    On Algorithms for $L$-bounded Cut Problem
    • P. Kolman
    • Mathematics, Computer Science
    • ArXiv
    • 2017
    • 2
    • PDF
    Parameterized complexity of length-bounded cuts and multi-cuts
    • 15
    Paths of bounded length and their cuts: Parameterized complexity and algorithms
    • 43
    • PDF
    Tree-depth, subgraph coloring and homomorphism bounds
    • 215
    • PDF
    Structural Parameterizations of the Mixed Chinese Postman Problem
    • 25
    • PDF
    On the directed hop-constrained shortest path problem
    • 56
    Length-bounded cuts and flows
    • 67
    • PDF