Skip to main content
SpringerLink
Log in

A Survey of Graph Algorithms Under Extended Streaming Models of Computation

  • Chapter
Fundamental Problems in Computing

Abstract

There has been a great deal of recent interest in the streaming model of computation where algorithms are restricted to a single pass over the data and have significantly less internal memory available than would be required to store the entire stream of data. Because of the inherent difficulty of solving graph problems in the streaming model, a number of extensions to the streaming model have been considered, namely the Semi-Streaming model, the W-Stream model, and the Stream-Sort model. In this chapter, we survey the algorithms developed for graph problems in each of these models. The survey is intended to be tutorial in nature although familiarity with graph algorithms is assumed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Aggarwal, M. Datar, S. Rajagopalan, and M. Ruhl. On the streaming model augmented with a sorting primitive. In Proc. 45th Annual IEEE Symp. Foundations of Computer Science (FOCS’04), pages 540–549, Rome, Italy, 2004.

    Google Scholar 

  2. N. Alon, Y. Matias, and M. Szegedy. The space complexity of approximating the frequency moments. J. Computer and System Sciences, 58(1):137–147, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  3. B. Babcock, S. Babu, M. Datar, R. Motwani, and J. Widom. Models and issues in data stream systems. In Proc. 21st ACM SIGMOD-SIGACT-SIGART Symp. Principles of Database Systems, pages 1–16, Madison, WI, 2002.

    Google Scholar 

  4. Z. Bar-Yossef, R. Kumar, and D. Sivakumar. Reductions in streaming algorithms, with an application to counting triangles in graphs. In Proc. 13th Annual ACM-SIAM Symp. Discrete Algorithms, pages 623–632, San Francisco, CA, 2002.

    Google Scholar 

  5. Z. Bar-Yossef, T. Jayram, R. Kumar, and D. Sivakumar. An information statistics approach to data stream and communication complexity. J. Computer and System Sciences, 68(4):702–732, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  6. A. L. Buchsbaum, R. Giancarlo, and J. R. Westbrook. On finding common neighborhoods in massive graphs. Theoretical Computer Science, 299(1-3):707–718, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  7. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein. Introduction to algorithms. McGraw–Hill/MIT Press, Cambridge, 2001.

    MATH  Google Scholar 

  8. C. Demetrescu, I. Finocchi, and A. Ribichini. Trading off space for passes in graph streaming problems. In Proc. 17th Annual ACM-SIAM Symp. Discrete Algorithms, pages 714–723, Miami, FL, 2006.

    Google Scholar 

  9. M. Elkin and J. Zhang. Efficient algorithms for constructing (1+ε, β)-spanners in the distributed and streaming models. In Proc. 23rd Annual ACM Symp. Principles of Distributed Computing, pages 160–168, St. John’s, Canada, 2004.

    Google Scholar 

  10. D. Eppstein, Z. Galil, G. F. Italiano, and A. Nissenzweig. Sparsification: a technique for speeding up dynamic graph algorithms. J. ACM, 44(5):669–696, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  11. J. Feigenbaum, S. Kannan, A. McGregor, S. Suri, and J. Zhang. Graph distances in the streaming model: the value of space. In Proc. 16th Annual ACM-SIAM Symp. Discrete Algorithms, pages 745–754, Vancouver, Canada, 2005.

    Google Scholar 

  12. J. Feigenbaum, S. Kannan, A. McGregor, S. Suri, and J. Zhang. On graph problems in a semi-streaming model. Theoretical Computer Science, 348(2-3):207–216, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  13. R. Guha, R. Kumar, D. Sivakumar, and R. Sundaram. Unweaving a web of documents. In Proc. 11th ACM SIGKDD Intl. Conf. Knowledge Discovery in Data Mining, pages 574–579, Chicago, IL, 2005.

    Google Scholar 

  14. M. Henzinger, P. Raghavan, and S. Rajagopalan. Computing on data streams. In External Memory Algorithms. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, volume 50, pages 107–118. American Mathematical Society, Providence, 2000.

    Google Scholar 

  15. D. E. Knuth. Sorting and Searching. The Art of Computer Programming, volume 3. Addison–Wesley–Longman, Redwood City, 2nd edition, 1998.

    Google Scholar 

  16. E. Kushilevitz and N. Nisan. Communication Complexity. Cambridge University Press, New York, 1996.

    Google Scholar 

  17. J. I. Munro and M. S. Paterson. Selection and sorting with limited storage. Theoretical Computer Science, 12(3):315–323, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  18. S. Muthukrishnan. Data streams: algorithms and applications. In Proc. 14th Annual ACM-SIAM Symp. Discrete Algorithms, page 413, Baltimore, MD, 2003.

    Google Scholar 

  19. L. Page, S. Brin, R. Motwani, and T. Winograd. The pagerank citation ranking: Bringing order to the web. Technical Report 1999-66, Stanford Digital Libraries, Nov. 1999.

    Google Scholar 

  20. M. Ruhl. Efficient algorithms for new computational models. PhD Thesis, Department of Computer Science, MIT, Cambridge, MA, 2003.

    Google Scholar 

  21. R. E. Tarjan. Data Structures and Network Algorithms. SIAM, Philadelphia, 1983.

    Google Scholar 

  22. R. Uehara and Z. Chen. Parallel approximation algorithms for maximum weighted matching in general graphs. Information Processing Letters, 76(1-2):13–17, 2000.

    Article  MathSciNet  Google Scholar 

  23. J. S. Vitter. External memory algorithms and data structures: Dealing with massive data. ACM Computing Surveys, 33(2):209–271, 2001.

    Article  Google Scholar 

  24. A. C. Yao. Some complexity questions related to distributive computing (preliminary report). In Proc. 11th Annual ACM Symp. Theory of Computing, pages 209–213, Atlanta, GA, Apr.–May 1979.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Skidmore College, Saratoga Springs, NY, 12866, USA

    Thomas C. O’Connell

Authors
  1. Thomas C. O’Connell
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas C. O’Connell .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University at Albany—SUNY, 1400 Washington Avenue, Albany, NY, 12222, USA

    S. S. Ravi

  2. Bradley Dept. Electrical and Computer Engineering, Virginia Tech, 302 Whittemore (0111), Blacksburg, VA, 24061, USA

    Sandeep K. Shukla

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science + Business Media B.V.

About this chapter

Cite this chapter

O’Connell, T.C. (2009). A Survey of Graph Algorithms Under Extended Streaming Models of Computation. In: Ravi, S.S., Shukla, S.K. (eds) Fundamental Problems in Computing. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9688-4_17

Download citation

  • DOI: https://doi.org/10.1007/978-1-4020-9688-4_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-9687-7

  • Online ISBN: 978-1-4020-9688-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation