Improved Approximation Algorithms for Hitting 3-Vertex Paths

  • Samuel Fiorini
  • Gwenaël JoretEmail author
  • Oliver Schaudt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9682)


We study the problem of deleting a minimum cost set of vertices from a given vertex-weighted graph in such a way that the resulting graph has no induced path on three vertices. This problem is often called cluster vertex deletion in the literature and admits a straightforward 3-approximation algorithm since it is a special case of the vertex cover problem on a 3-uniform hypergraph. Very recently, You et al. [14] described an efficient 5/2-approximation algorithm for the unweighted version of the problem. Our main result is a 7/3-approximation algorithm for arbitrary weights, using the local ratio technique. We further conjecture that the problem admits a 2-approximation algorithm and give some support for the conjecture. This is in sharp constrast with the fact that the similar problem of deleting vertices to eliminate all triangles in a graph is known to be UGC-hard to approximate to within a ratio better than 3, as proved by Guruswami and Lee [7].


Weighted Graph Vertex Cover Subgraph Isomorphic Vertex Cover Problem Local Ratio 
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 International Publishing Switzerland 2016

Authors and Affiliations

  • Samuel Fiorini
    • 1
  • Gwenaël Joret
    • 2
    Email author
  • Oliver Schaudt
    • 3
  1. 1.Département de MathématiqueUniversité libre de BruxellesBrusselsBelgium
  2. 2.Département d’InformatiqueUniversité libre de BruxellesBrusselsBelgium
  3. 3.Institut für InformatikUniversität zu KölnKölnGermany

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