NC algorithms for partitioning planar graphs into induced forests and approximating NP-hard problems

  • Zhi-Zhong Chen
  • Xin He
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1017)


It is well known that the vertex set of every planar graph can be partitioned into three subsets each of which induces a forest. Previously, there has been no NC algorithm for computing such a partition. In this paper, we design an optimal NC algorithm for computing such a partition for a given planar graph. It runs in O(log n log*n) time using O(n/(log n log*n)) processors on an EREW PRAM. This algorithm implies optimal NC approximation algorithms for many NP-hard maximum induced subgraph problems on planar graphs with a performance ratio of 3. We also present optimal NC algorithms for partitioning the vertex set of a given K4-free or K2, 3-free graph into two subsets each of which induces a forest. As consequences,we obtain optimal NC algorithms for 4-coloring K4-free or K2, 3-free graphs which are previously unknown to our knowledge.


Planar Graph Parallel Algorithm Performance Ratio Adjacency List Hamiltonian Circuit 
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 1995

Authors and Affiliations

  • Zhi-Zhong Chen
    • 1
  • Xin He
    • 2
  1. 1.Dept. of Mathematical SciencesTokyo Denki UniversitySaitamaJapan
  2. 2.Dept. of Computer ScienceState Univ. of New York at BuffaloBuffaloUSA

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