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

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LATIN 2016: Theoretical Informatics (LATIN 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9644))

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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.

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Notes

  1. 1.

    For instance, “we take \(S_1\) plus the \(k_2\) best vertices in \(V_2\)” means that we take \(S_1\) and then \(k_2\) vertices of highest degree in \(B[(V_1 \setminus S_1),V_2]\).

References

  1. Apollonio, N., Simeone, B.: The maximum vertex coverage problem on bipartite graphs. Discrete Appl. Math. 165, 37–48 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  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. Hochbaum, D.S., Pathria, A.: Analysis of the greedy approach in problems of maximum \(k\)-coverage. Naval Res. Logistics 45, 615–627 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  6. Petrank, E.: The hardness of approximation: gap location. Comput. Complex. 4, 133–157 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  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. Feige, U., Karpinski, M., Langberg, M.: Improved approximation of max-cut on graphs of bounded degree. J. Algorithms 43, 201–219 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  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. Frank, M., Wolfe, P.: An algorithm for quadratic programming. Naval Res. Logistics Q. 3, 95–110 (1956)

    Article  MathSciNet  Google Scholar 

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Acknowledgement

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

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Authors and Affiliations

  1. Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI), Budapest, Hungary

    Édouard Bonnet

  2. Sorbonne Universités, UPMC Universite Paris 06, CNRS, LIP6 UMR 7606, Paris, France

    Bruno Escoffier

  3. PSL* Research University, Université Paris-Dauphine, LAMSADE, Paris, France

    Vangelis Th. Paschos & Georgios Stamoulis

  4. CNRS UMR 7243, Paris, France

    Vangelis Th. Paschos & Georgios Stamoulis

Authors
  1. Édouard Bonnet
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  2. Bruno Escoffier
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  3. Vangelis Th. Paschos
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  4. Georgios Stamoulis
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Corresponding author

Correspondence to Vangelis Th. Paschos .

Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, ON, Ontario, Canada

    Evangelos Kranakis

  2. University Chile, Santiago, Chile

    Gonzalo Navarro

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Bonnet, É., Escoffier, B., Paschos, V.T., Stamoulis, G. (2016). A 0.821-Ratio Purely Combinatorial Algorithm for Maximum k-vertex Cover in Bipartite Graphs. In: Kranakis, E., Navarro, G., Chávez, E. (eds) LATIN 2016: Theoretical Informatics. LATIN 2016. Lecture Notes in Computer Science(), vol 9644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49529-2_18

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  • DOI: https://doi.org/10.1007/978-3-662-49529-2_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-49528-5

  • Online ISBN: 978-3-662-49529-2

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