Advertisement

Best-Order Streaming Model

  • Atish Das Sarma
  • Richard J. Lipton
  • Danupon Nanongkai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5532)

Abstract

We study a new model of computation called stream checking on graph problems where a space-limited verifier has to verify a proof sequentially (i.e., it reads the proof as a stream). Moreover, the proof itself is nothing but a reordering of the input data. This model has a close relationship to many models of computation in other areas such as data streams, communication complexity, and proof checking and could be used in applications such as cloud computing.

In this paper we focus on graph problems where the input is a sequence of edges. We show that checking if a graph has a perfect matching is impossible to do deterministically using small space. To contrast this, we show that randomized verifiers are powerful enough to check whether a graph has a perfect matching or is connected.

Keywords

Cloud Computing Perfect Match Hamiltonian Cycle Communication Complexity Deterministic 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.
    Amazon elastic compute cloud (amazon ec2)Google Scholar
  2. 2.
    Aggarwal, G., Datar, M., Rajagopalan, S., Ruhl, M.: On the streaming model augmented with a sorting primitive. In: Annual IEEE Symposium on Foundations of Computer Science, pp. 540–549 (2004)Google Scholar
  3. 3.
    Alon, N., Matias, Y., Szegedy, M.: The space complexity of approximating the frequency moments. J. Comput. Syst. Sci. 58(1), 137–147 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Arora, S., Lund, C., Motwani, R., Sudan, M., Szegedy, M.: Proof verification and the hardness of approximation problems. J. ACM 45(3), 501–555 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Arora, S., Safra, S.: Probabilistic checking of proofs: A new characterization of np. J. ACM 45(1), 70–122 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Chakrabarti, A., Cormode, G., McGregor, A.: Robust lower bounds for communication and stream computation. In: STOC, pp. 641–650 (2008)Google Scholar
  7. 7.
    Chakrabarti, A., Jayram, T.S., Pǎtraşcu, M.: Tight lower bounds for selection in randomly ordered streams. In: Proc. 19th ACM/SIAM Symposium on Discrete Algorithms (SODA), pp. 720–729 (2008)Google Scholar
  8. 8.
    Demetrescu, C., Finocchi, I., Ribichini, A.: Trading off space for passes in graph streaming problems. In: SODA 2006: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm, pp. 714–723. ACM, New York (2006)CrossRefGoogle Scholar
  9. 9.
    Dinur, I.: The pcp theorem by gap amplification. J. ACM 54(3), 12 (2007)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Feigenbaum, J., Kannan, S., Strauss, M., Viswanathan, M.: Testing and spot-checking of data streams (extended abstract). In: SODA 2000: Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms, Philadelphia, PA, USA, pp. 165–174. Society for Industrial and Applied Mathematics (2000)Google Scholar
  11. 11.
    Feigenbaum, J., Kannan, S., McGregor, A., Suri, S., Zhang, J.: Graph distances in the streaming model: the value of space. In: SODA 2005: Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms, Philadelphia, PA, USA, pp. 745–754. Society for Industrial and Applied Mathematics (2005)Google Scholar
  12. 12.
    Feigenbaum, J., Kannan, S., McGregor, A., Suri, S., Zhang, J.: On graph problems in a semi-streaming model. Theor. Comput. Sci. 348(2), 207–216 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Goldreich, O.: Property testing in massive graphs, pp. 123–147 (2002)Google Scholar
  14. 14.
    Gopalan, P., Radhakrishnan, J.: Finding duplicates in a data stream. In: SODA 2009: Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms, Philadelphia, PA, USA. Society for Industrial and Applied Mathematics (to appear, 2009)Google Scholar
  15. 15.
    Guha, S., McGregor, A.: Approximate quantiles and the order of the stream. In: PODS 2006: Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems, pp. 273–279. ACM, New York (2006)CrossRefGoogle Scholar
  16. 16.
    Guha, S., Mcgregor, A.: Lower bounds for quantile estimation in random-order and multi-pass streaming. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 704–715. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  17. 17.
    Hajnal, A., Maass, W., Turán, G.: On the communication complexity of graph properties. In: STOC, pp. 186–191 (1988)Google Scholar
  18. 18.
    Håstad, J., Wigderson, A.: The randomized communication complexity of set disjointness. Theory of Computing 3(1), 211–219 (2007)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Henzinger, M.R., Raghavan, P., Rajagopalan, S.: Computing on data streams, pp. 107–118 (1999)Google Scholar
  20. 20.
    Kushilevitz, E., Nisan, N.: Communication complexity. Cambridge University Press, New York (1997)zbMATHGoogle Scholar
  21. 21.
    Lam, T.W., Ruzzo, W.L.: Results on communication complexity classes. J. Comput. Syst. Sci. 44(2), 324–342 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Lipton, R.J.: Fingerprinting sets. Cs-tr-212-89. Princeton University (1989)Google Scholar
  23. 23.
    Lipton, R.J.: Efficient checking of computations. In: STACS, pp. 207–215 (1990)Google Scholar
  24. 24.
    Munro, J.I., Paterson, M.: Selection and sorting with limited storage. In: FOCS, pp. 253–258 (1978)Google Scholar
  25. 25.
    Papadimitriou, C.H., Sipser, M.: Communication complexity. J. Comput. Syst. Sci. 28(2), 260–269 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Ruhl, J.M.: Efficient algorithms for new computational models. Ph.D thesis, Supervisor-David R. Karger (2003)Google Scholar
  27. 27.
    Yao, A.C.-C.: Some complexity questions related to distributive computing (preliminary report). In: STOC, pp. 209–213 (1979)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Atish Das Sarma
    • 1
  • Richard J. Lipton
    • 1
  • Danupon Nanongkai
    • 1
  1. 1.Georgia Institute of Technology 

Personalised recommendations