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A 0.821-Ratio Purely Combinatorial Algorithm for Maximum k-vertex Cover in Bipartite Graphs

  • Édouard Bonnet
  • Bruno Escoffier
  • Vangelis Th. PaschosEmail author
  • Georgios Stamoulis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9644)

Abstract

We study the polynomial time approximation of the max k-vertex cover problem in bipartite graphs and propose a purely combinatorial algorithm that beats the only such known algorithm, namely the greedy approach. We present a computer-assisted analysis of our algorithm, establishing that the worst case approximation guarantee is bounded below by 0.821.

Notes

Acknowledgement

The work of the last author was supported by the Swiss National Research Foundation Early Post-Doc mobility grant P1TIP2_152282.

References

  1. 1.
    Apollonio, N., Simeone, B.: The maximum vertex coverage problem on bipartite graphs. Discrete Appl. Math. 165, 37–48 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Caskurlu, B., Mkrtchyan, V., Parekh, O., Subramani, K.: On partial vertex cover and budgeted maximum coverage problems in bipartite graphs. In: Diaz, J., Lanese, I., Sangiorgi, D. (eds.) TCS 2014. LNCS, vol. 8705, pp. 13–26. Springer, Heidelberg (2014)Google Scholar
  3. 3.
    Hochbaum, D.S., Pathria, A.: Analysis of the greedy approach in problems of maximum \(k\)-coverage. Naval Res. Logistics 45, 615–627 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Badanidiyuru, A., Kleinberg, R., Lee, H.: Approximating low-dimensional coverage problems. In: Dey, T.K., Whitesides, S. (eds.) SoCG 2012, pp. 161–170. ACM, Chapel Hill (2012)Google Scholar
  5. 5.
    Ageev, A.A., Sviridenko, M.I.: Approximation algorithms for maximum coverage and max cut with given sizes of parts. In: Cornuéjols, G., Burkard, R.E., Woeginger, G.J. (eds.) IPCO 1999. LNCS, vol. 1610, p. 17. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  6. 6.
    Petrank, E.: The hardness of approximation: gap location. Comput. Complex. 4, 133–157 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Bonnet, E., Escoffier, B., Paschos, V.T., Stamoulis, G.: A 0.821-ratio purely combinatorial algorithm for maximum \(k\)-vertex cover in bipartite graphs. CoRR arXiv:1409.6952v2 (2015)
  8. 8.
    Feige, U., Karpinski, M., Langberg, M.: Improved approximation of max-cut on graphs of bounded degree. J. Algorithms 43, 201–219 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Abadie, J., Carpentier, J.: Generalization of the wolfe reduced gradient method to the case of non-linear constraints. In: Abadie, J., Carpentier, J. (eds.) Optimization. Academic Publishers (1969)Google Scholar
  10. 10.
    Frank, M., Wolfe, P.: An algorithm for quadratic programming. Naval Res. Logistics Q. 3, 95–110 (1956)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Édouard Bonnet
    • 1
  • Bruno Escoffier
    • 2
  • Vangelis Th. Paschos
    • 3
    • 4
    Email author
  • Georgios Stamoulis
    • 3
    • 4
  1. 1.Institute for Computer Science and ControlHungarian Academy of Sciences (MTA SZTAKI)BudapestHungary
  2. 2.Sorbonne Universités, UPMC Universite Paris 06, CNRS, LIP6 UMR 7606ParisFrance
  3. 3.PSL* Research University, Université Paris-Dauphine, LAMSADEParisFrance
  4. 4.CNRS UMR 7243ParisFrance

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