Solving Planar k-Terminal Cut in \(O(n^{c \sqrt{k}})\) Time

  • Philip N. Klein
  • Dániel Marx
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7391)


The problem Planar k -Terminal Cut is as follows: given an undirected planar graph with edge-costs and with k vertices designated as terminals, find a minimum-cost set of edges whose removal pairwise separates the terminals. It was known that the complexity of this problem is O(n 2k − 4logn). We show that there is a constant c such that the complexity is \(O(n^{c\sqrt{k}})\). This matches a recent lower bound of Marx showing that the \(c\sqrt{k}\) term in the exponent is best possible up to the constant c (assuming the Exponential Time Hypothesis).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Philip N. Klein
    • 1
  • Dániel Marx
    • 2
  1. 1.Computer Science DepartmentBrown UniversityProvidenceUSA
  2. 2.Computer and Automation Research InstituteHungarian Academy of Sciences (MTA SZTAKI)BudapestHungary

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