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Matching and P 2-Packing: Weighted Versions

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Book cover Computing and Combinatorics (COCOON 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6842))

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Abstract

Parameterized algorithms are presented for the weighted P 2-Packing problem, which is a generalization of the famous Graph Matching problem. The algorithms are based on the following new techniques and observations: (1) new study on structure relationship between graph matchings in general graphs and P 2-packings in bipartite graphs; (2) an effective graph bi-partitioning algorithm; and (3) a polynomial-time algorithm for a constrained weighted P 2-Packing problem in bipartite graphs. These techniques lead to randomized and deterministic parameterized algorithms that significantly improve the previous best upper bounds for the problem for both weighted and unweighted versions.

This work is supported by the National Natural Science Foundation of China under Grant (61073036, 61070224), the Doctoral Discipline Foundation of Higher Education Institution of China under Grant (20090162110056).

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References

  1. Bar-Yehuda, R., Halldórsson, M., Naor, J., Shachnai, H., Shapira, I.: Scheduling split intervals. In: Proc. 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 732–741. ACM Press, New York (2002)

    Google Scholar 

  2. Bazgan, C., Hassin, R., Monnot, J.: Approximation algorithms for some vehicle routing problems. Discrete Appl. Math. 146, 27–42 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen, J., Lu, S.: Improved parameterized set splitting algorithms: A probabilistic approach. Algorithmica 54(4), 472–489 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. De Bontridder, K., Halldórsson, B., Lenstra, J., Ravi, R., Stougie, L.: Approximation algorithms for the test cover problem. Math. Program, Ser. B 98, 477–491 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Fellows, M., Heggernes, P., Rosamond, F., Sloper, C., Telle, J.A.: Exact algorithms for finding k disjoint triangles in an arbitrary graph. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds.) WG 2004. LNCS, vol. 3353, pp. 235–244. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  6. Feng, Q., Liu, Y., Lu, S., Wang, J.: Improved deterministic algorithms for weighted matching and packing problems. In: Chen, J., Cooper, S.B. (eds.) TAMC 2009. LNCS, vol. 5532, pp. 211–220. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  7. Gabow, H.: Data structures for weighted matching and nearest common ancestoers. In: Proc. 1st Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 434–443. ACM Press, New York (1990)

    Google Scholar 

  8. Fernau, H., Raible, D.: A parameterized perspective on packing paths of length two. Journal of Combinatorial Optimization 18(4), 319–341 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hassin, R., Rubinstein, S.: An approximation algorithm for maximum triangle packing. Discrete Appl. Math. 154, 971–979 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hell, P., Kirkpatrick, D.: On the complexity of a generalized matching problem. In: Mitzenmacher, M. (ed.) Proc. 10th Annual ACM Symposium on Theory of Computing, pp. 240–245. ACM Press, New York (1978)

    Google Scholar 

  11. Hurkens, C., Schrijver, A.: On the size of systems of sets every t of which have an SDR, with application to worst case ratio of heuristics for packing problems. SIAM Journal on Discrete Mathmatics 2, 68–72 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kann, V.: Maximum bounded H-matching is MAX-SNP-complete. Information Processing Letters 49, 309–318 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  13. Koutis, I.: Faster algebraic algorithms for path and packing problems. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 575–586. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  14. Kirkpatrick, D.G., Hell, P.: On the complexity of general graph factor problems. SIAM Journal on Computing 12, 601–609 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  15. van Leeuwen, J.: Graph algorithms. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. A, pp. 525–631 (1990)

    Google Scholar 

  16. Monnot, J., Toulouse, S.: The P k partitioning problem and related problems in bipartite graphs. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds.) SOFSEM 2007. LNCS, vol. 4362, pp. 422–433. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  17. Naor, M., Schulman, L., Srinivasan, A.: Splitters and near-optimal derandomization. In: Proc. 39th Annual Symposium on Foundatins of Computer Science, pp. 182–190. IEEE Press, New York (1995)

    Google Scholar 

  18. Prieto, E., Sloper, C.: Looking at the stars. Theoretical Computer Science 351, 437–445 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  19. Wang, J., Feng, Q.: An O *(3.523k) parameterized algorithm for 3-set packing. In: Agrawal, M., Du, D.-Z., Duan, Z., Li, A. (eds.) TAMC 2008. LNCS, vol. 4978, pp. 82–93. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  20. Wang, J., Ning, D., Feng, Q., Chen, J.: An improved parameterized algorithm for a generalized matching problem. In: Agrawal, M., Du, D.-Z., Duan, Z., Li, A. (eds.) TAMC 2008. LNCS, vol. 4978, pp. 212–222. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Central South University, Changsha, 410083, P.R. China

    Qilong Feng, Jianxin Wang & Jianer Chen

  2. Department of Computer Science and Engineering, Texas A&M University College Station, Texas, 77843-3112, USA

    Jianer Chen

Authors
  1. Qilong Feng
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  2. Jianxin Wang
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  3. Jianer Chen
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas-Pan American, 78539, Edinburg, TX, USA

    Bin Fu

  2. Department of Computer Science, University of Texas at Dallas, 75080, Richardson, TX, USA

    Ding-Zhu Du

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Feng, Q., Wang, J., Chen, J. (2011). Matching and P 2-Packing: Weighted Versions. In: Fu, B., Du, DZ. (eds) Computing and Combinatorics. COCOON 2011. Lecture Notes in Computer Science, vol 6842. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22685-4_31

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  • DOI: https://doi.org/10.1007/978-3-642-22685-4_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22684-7

  • Online ISBN: 978-3-642-22685-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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