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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)

Abstract

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).

Keywords

Steiner Tree Interior Edge Blue Edge Label Structure Branch Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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