Algorithms for Cut Problems on Trees

  • Iyad Kanj
  • Guohui Lin
  • Tian Liu
  • Weitian Tong
  • Ge Xia
  • Jinhui Xu
  • Boting Yang
  • Fenghui Zhang
  • Peng Zhang
  • Binhai Zhu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8881)


We study the multicut on trees and the generalized multiway cut on trees problems. For the multicut on trees problem, we present a parameterized algorithm that runs in time \(O^{*}(\rho ^k)\), where \(\rho = \sqrt{\sqrt{2} + 1} \approx 1.555\) is the positive root of the polynomial \(x^4-2x^2-1\). This improves the current-best algorithm of Chen et al. that runs in time \(O^{*}(1.619^k)\). By reducing generalized multiway cut on trees to multicut on trees, our results give a parameterized algorithm that solves the generalized multiway cut on trees problem in time \(O^{*}(\rho ^k)\). We also show that the generalized multiway cut on trees problem is solvable in polynomial time if the number of terminal sets is a fixed constant.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Iyad Kanj
    • 1
  • Guohui Lin
    • 2
  • Tian Liu
    • 3
  • Weitian Tong
    • 2
  • Ge Xia
    • 4
  • Jinhui Xu
    • 5
  • Boting Yang
    • 6
  • Fenghui Zhang
    • 7
  • Peng Zhang
    • 8
  • Binhai Zhu
    • 9
  1. 1.School of ComputingDePaul UniversityChicagoUSA
  2. 2.Department of Computing ScienceUniversity of AlbertaEdmontonCanada
  3. 3.School of Electronic Engineering and Computer SciencePeking UniversityBeijingChina
  4. 4.Department of Computing ScienceLafayette collegeEastonUSA
  5. 5.Department of Computer Science and EngineeringState University of New York at Buffalo (SUNY Buffalo)BuffaloUSA
  6. 6.Department of Computer ScienceUniversity of ReginaReginaCanada
  7. 7.Google KirklandKirklandUSA
  8. 8.School of Computer Science and TechnologyShandong UniversityJinanChina
  9. 9.Department of Computer ScienceMontana State UniversityBozemanUSA

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