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A Linear Edge Kernel for Two-Layer Crossing Minimization

  • Yasuaki Kobayashi
  • Hirokazu Maruta
  • Yusuke Nakae
  • Hisao Tamaki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7936)

Abstract

We consider a simple generalization of two-layer crossing minimization problem (TLCM) called leaf-edge-weighted TLCM (LEW-TLCM), where we allow positive weights on edges incident to leaves, and show that this problem admits a kernel with O(k) edges provided that the given graph is connected. As a straightforward consequence, LEW-TLCM (and hence TLCM) has a fixed parameter algorithm that runs in 2 O(k logk) + n O(1) time which improves on the previously best known algorithm with running time \(2^{O(k^3)}n\).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Yasuaki Kobayashi
    • 1
  • Hirokazu Maruta
    • 1
  • Yusuke Nakae
    • 1
  • Hisao Tamaki
    • 1
  1. 1.Meiji UniversityKawasakiJapan

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