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.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Edmonds, J.: Maximum matching and a polyhedron with 0,1-vertices. J. Res. Nat. Bur. Standards 69, 125–130 (1965)
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)
Hopcroft, J.E., Karp, R.M.: An n5/2 algorithm for maximum matchings in bipartite graphs. SIAM J. Comput. 2, 225–231 (1973)
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)
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)
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)
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)
Muthukrishnan, S.: Data streams: Algorithms and applications (2003), available at http://athos.rutgers.edu/~muthu/stream-1-1.ps
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)
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)
Munro, J., Paterson, M.: Selection and sorting with limited storage. Theoretical Computer Science 12, 315–323 (1980)
Henzinger, M.R., Raghavan, P., Rajagopalan, S.: Computing on data streams. Technical Report 1998-001, DEC Systems Research Center (1998)
Alon, N., Matias, Y., Szegedy, M.: The space complexity of approximating the frequency moments. Journal of Computer and System Sciences 58, 137–147 (1999)
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)
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)
Drineas, P., Kannan, R.: Pass efficient algorithms for approximating large matrices. In: Proc. 14th ACM-SIAM Symposium on Discrete Algorithms, pp. 223–232 (2003)
Buchsbaum, A.L., Giancarlo, R., Westbrook, J.: On finding common neighborhoods in massive graphs. Theor. Comput. Sci. 1-3, 707–718 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
McGregor, A. (2005). Finding Graph Matchings in Data Streams. In: Chekuri, C., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds) Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2005 2005. Lecture Notes in Computer Science, vol 3624. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11538462_15
Download citation
DOI: https://doi.org/10.1007/11538462_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28239-6
Online ISBN: 978-3-540-31874-3
eBook Packages: Computer ScienceComputer Science (R0)