Advertisement

Abstract

We present algorithms for finding large graph matchings in the streaming model. In this model, applicable when dealing with massive graphs, edges are streamed-in in some arbitrary order rather than residing in randomly accessible memory. For ε> 0, we achieve a \(\frac1{1+\epsilon}\) approximation for maximum cardinality matching and a \(\frac1{2+\epsilon}\) approximation to maximum weighted matching. Both algorithms use a constant number of passes and \(\tilde O(|V|)\) space.

Keywords

Data Stream Maximal Match Find Graph Free Vertex Pass Algorithm 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Edmonds, J.: Maximum matching and a polyhedron with 0,1-vertices. J. Res. Nat. Bur. Standards 69, 125–130 (1965)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Gabow, H.N.: Data structures for weighted matching and nearest common ancestors with linking. In: Proc. ACM-SIAM Symposium on Discrete Algorithms, pp. 434–443 (1990)Google Scholar
  3. 3.
    Hopcroft, J.E., Karp, R.M.: An n5/2 algorithm for maximum matchings in bipartite graphs. SIAM J. Comput. 2, 225–231 (1973)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Micali, S., Vazirani, V.: An O(\(\sqrt{V}\) E) algorithm for finding maximum matching in general graphs. In: Proc. 21st Annual IEEE Symposium on Foundations of Computer Science (1980)Google Scholar
  5. 5.
    Drake, D.E., Hougardy, S.: Improved linear time approximation algorithms for weighted matchings. In: Arora, S., Jansen, K., Rolim, J.D.P., Sahai, A. (eds.) RANDOM 2003 and APPROX 2003. LNCS, vol. 2764, pp. 14–23. Springer, Heidelberg (2003)Google Scholar
  6. 6.
    Kalantari, B., Shokoufandeh, A.: Approximation schemes for maximum cardinality matching. Technical Report LCSR–TR–248, Laboratory for Computer Science Research, Department of Computer Science. Rutgers University (1995)Google Scholar
  7. 7.
    Preis, R.: Linear time 1/2-approximation algorithm for maximum weighted matching in general graphs. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 259–269. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  8. 8.
    Muthukrishnan, S.: Data streams: Algorithms and applications (2003), available at http://athos.rutgers.edu/~muthu/stream-1-1.ps
  9. 9.
    Feigenbaum, J., Kannan, S., McGregor, A., Suri, S., Zhang, J.: On graph problems in a semi-streaming model. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 531–543. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Feigenbaum, J., Kannan, S., McGregor, A., Suri, S., Zhang, J.: Graph distances in the streaming model: The value of space. Proc. 16th ACM-SIAM Symposium on Discrete Algorithms (2005)Google Scholar
  11. 11.
    Munro, J., Paterson, M.: Selection and sorting with limited storage. Theoretical Computer Science 12, 315–323 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Henzinger, M.R., Raghavan, P., Rajagopalan, S.: Computing on data streams. Technical Report 1998-001, DEC Systems Research Center (1998)Google Scholar
  13. 13.
    Alon, N., Matias, Y., Szegedy, M.: The space complexity of approximating the frequency moments. Journal of Computer and System Sciences 58, 137–147 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Feigenbaum, J., Kannan, S., Strauss, M., Viswanathan, M.: An approximate L1 difference algorithm for massive data streams. SIAM Journal on Computing 32, 131–151 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Guha, S., Mishra, N., Motwani, R., O’Callaghan, L.: Clustering data streams. In: Proc. 41th IEEE Symposium on Foundations of Computer Science, pp. 359–366 (2000)Google Scholar
  16. 16.
    Drineas, P., Kannan, R.: Pass efficient algorithms for approximating large matrices. In: Proc. 14th ACM-SIAM Symposium on Discrete Algorithms, pp. 223–232 (2003)Google Scholar
  17. 17.
    Buchsbaum, A.L., Giancarlo, R., Westbrook, J.: On finding common neighborhoods in massive graphs. Theor. Comput. Sci. 1-3, 707–718 (2003)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Andrew McGregor
    • 1
  1. 1.Department of Computer and Information ScienceUniversity of PennsylvaniaPhiladelphiaUSA

Personalised recommendations