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International Computing and Combinatorics Conference

COCOON 2018: Computing and Combinatorics pp 726–737Cite as

Constant Factor Approximation Algorithm for l-Pseudoforest Deletion Problem

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10976))

Abstract

An l-pseudoforest is a graph each of whose connected component is at most l edges away from being a tree. The l-Pseudoforest Deletion problem is to delete a vertex set P of minimum weight from a given vertex-weighted graph \(G=(V,E)\) such that the remaining graph \(G[V\setminus P]\) is an l-pseudoforest. The Feedback Vertex Set problem is a special case of the l-Pseudoforest Deletion problem with \(l=0\). In this paper, we present a polynomial time 4l-approximation algorithm for the l-Pseudoforest Deletion problem with \(l\ge 1\) by using the local ratio technique. When \(l=1\), we get a better approximation ratio 2 for the problem by further analyzing the algorithm, which matches the current best constant approximation factor for the Feedback Vertex Set problem.

This work is supported by the National Natural Science Foundation of China under Grants (61772179, 61472449, 61420106009, 61402054), the Science and Technology Plan Project of Hunan Province under Grant (2016TP1020) and the Scientific Research Fund of Hunan Provincial Education Department under Grant (17C0222).

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References

  1. Bafana, V., Berman, P., Fujito, T.: A 2-approximation algorithm for the undirected feedback vertex set problem. SIAM J. Discret. Math. 12(3), 289–297 (1999)

    Article  MathSciNet  Google Scholar 

  2. Bar-Yehuda, R., Even, S.: A local-ratio theorem for approximating the weighted vertex cover problem. Ann. Discret. Math. 25, 27–46 (1985)

    MathSciNet  MATH  Google Scholar 

  3. Becker, A., Geiger, D.: Optimization of Pearl’s method of conditioning and greedy-like approximation algorithms for the vertex feedback set problem. Artif. Intell. 83(1), 167–188 (1996)

    Article  MathSciNet  Google Scholar 

  4. Bodlaender, H.L., Ono, H., Otachi, Y.: A faster parameterized algorithm for pseudoforest deletion. In: Guo, J., Danny, H. (eds.) IPEC 2016, LIPIcs, Dagstuhl, Germany, vol. 63, pp. 7:1–7:12 (2017). https://doi.org/10.4230/LIPIcs.IPEC.2016.7

  5. Chudak, F.A., Goemans, M.X., Hochbaum, D.S., Williamson, D.P.: A primal-dual interpretation of two 2-approximation algorithms for the feedback vertex set problem in undirected graphs. Oper. Res. Lett. 22(4–5), 111–118 (1998)

    Article  MathSciNet  Google Scholar 

  6. Cygan, M., Nederlof, J., Pilipczuk, M., Pilipczuk, M., Rooij, J.M.M., Wojtaszczyk, J.O.: Solving connectivity problems parameterized by treewidth in single exponential time. In: FOCS 2011, pp. 150–159. IEEE Press, New York (2011). https://doi.org/10.1109/FOCS.2011.23

  7. Fomin, F.V., Lokshtanov, D., Misra, N., Saurabh, S.: Planar F-deletion: approximation, kernelization and optimal FPT algorithms. In: FOCS 2012, pp. 470–479. IEEE Press, New York (2012). https://doi.org/10.1109/FOCS.2012.62

  8. Fujito, T.: A note on approximation of the vertex cover and feedback vertex set problems - unified approach. Inf. Process. Lett. 59(2), 59–63 (1996)

    Article  MathSciNet  Google Scholar 

  9. Jansen, B.M., Raman, V., Vatshelle, M.: Parameter ecology for feedback vertex set. Tsinghua Sci. Technol. 19(4), 387–409 (2014)

    Article  MathSciNet  Google Scholar 

  10. Kociumaka, T., Pilipczuk, M.: Faster deterministic feedback vertex set. Inf. Process. Lett. 114(10), 556–560 (2014)

    Article  MathSciNet  Google Scholar 

  11. Lin, M., Feng, Q., Wang, J., Chen, J., Fu, B., Li, W.: An improved FPT algorithm for almost forest deletion problem. Inf. Process. Lett. 136, 30–36 (2018)

    Article  MathSciNet  Google Scholar 

  12. Majumdar, D.: Structural parameterizations of feedback vertex set. In: Guo J., Danny H. (eds.) IPEC 2016, LIPIcs, Dagstuhl, Germany, vol. 63, pp. 21:1–21:16 (2017). https://doi.org/10.4230/LIPIcs.IPEC.2016.21

  13. Philip, G., Rai, A., Saurabh, S.: Generalized pseudoforest deletion: algorithms and uniform kernel. In: Italiano, G.F., Pighizzini, G., Sannella, D.T. (eds.) MFCS 2015. LNCS, vol. 9235, pp. 517–528. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48054-0_43

    Chapter  Google Scholar 

  14. Rai, A., Saurabh, S.: Bivariate complexity analysis of Almost Forest Deletion. In: Xu, D., Du, D., Du, D. (eds.) COCOON 2015. LNCS, vol. 9198, pp. 133–144. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21398-9_11

    Chapter  Google Scholar 

  15. Rai, A.: Parameterized algorithms for graph modification problems. Ph.D. thesis, Homi Bhabha National Institute, Chennai, India (2016)

    Google Scholar 

  16. Xiao, M., Nagamochi, H.: An improved exact algorithm for undirected feedback vertex set. J. Comb. Optim. 30(2), 214–241 (2015)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Information Science and Engineering, Central South University, Changsha, China

    Mugang Lin & Qilong Feng

  2. School of Computer Science and Technology, Hengyang Normal University, Hengyang, China

    Mugang Lin

  3. Hunan Provincial Key Laboratory of Intelligent Information Processing and Application, Hengyang, China

    Mugang Lin

  4. Department of Computer Science, University of Texas Rio Grande Valley, Edinburg, TX, 78539, USA

    Bin Fu

Authors
  1. Mugang Lin
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  2. Bin Fu
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  3. Qilong Feng
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Corresponding author

Correspondence to Qilong Feng .

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Editors and Affiliations

  1. City University of Hong Kong, Hong Kong, China

    Lusheng Wang

  2. Shandong University, Jinan, China

    Daming Zhu

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Lin, M., Fu, B., Feng, Q. (2018). Constant Factor Approximation Algorithm for l-Pseudoforest Deletion Problem. In: Wang, L., Zhu, D. (eds) Computing and Combinatorics. COCOON 2018. Lecture Notes in Computer Science(), vol 10976. Springer, Cham. https://doi.org/10.1007/978-3-319-94776-1_60

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  • DOI: https://doi.org/10.1007/978-3-319-94776-1_60

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94775-4

  • Online ISBN: 978-3-319-94776-1

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