On Estimating Path Aggregates over Streaming Graphs

  • Sumit Ganguly
  • Barna Saha
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4288)


We consider the updatable streaming graph model, where edges of a graph arrive or depart in arbitrary sequence and are processed in an online fashion using sub-linear space and time. We study the problem of estimating aggregate path metrics P k defined as the number of pairs of vertices that have a simple path between them of length k. For a streaming undirected graph with n vertices, m edges and r components, we present an \(\tilde{O}(m(m-r)^{-1/4})\) space algorithm for estimating P 2 and an \(\Omega(\sqrt{m})\) space lower bound. We show that estimating P 2 over directed streaming graphs, and estimating P k over streaming graphs (whether directed or undirected), for any k ≥3 requires Ω(n 2) space. We also present a space lower bound of Ω(n 2) for the problems of (a) deterministically testing the connectivity, and, (b) estimating the size of transitive closure, of undirected streaming graphs that allow both edge-insertions and deletions.


Data Stream Connected Graph Transitive Closure Simple Path Adjacency List 
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  1. 1.
    Demetrescu, C., Finocchi, I., Ribichini, A.: Trading off space for passes in graph streaming problems. In: Proceedings of ACM SODA (2006)Google Scholar
  2. 2.
    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
  3. 3.
    Feigenbaum, J., Kannan, S., McGregor, A., Suri, S., Zhang, J.: Graph distances in the streaming model: the value of space. In: Proceedings of ACM SODA (2005)Google Scholar
  4. 4.
    Flajolet, P., Martin, G.N.: Probabilistic Counting Algorithms for Database Applications. J. Comp. Sys. and Sc. 31(2), 182–209 (1985)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Ganguly, S., Garofalakis, M.N., Kumar, A., Rastogi, R.: Join-distinct aggregate estimation over update streams. In: Proceedings of ACM PODS (2005)Google Scholar
  6. 6.
    Gibbons, P.B., Tirthapura, S.: Estimating simple functions on the union of data streams. In: Proceedings of ACM SPAA (2001)Google Scholar
  7. 7.
    Henzinger, M., Raghavan, P., Rajagopalan, S.: Computing on data streams. Technical Note 1998-011, Digital Systems Research, Palo Alto, CA (May 1998)Google Scholar
  8. 8.
    Muthukrishnan, S.: Data Streams: Algorithms and Applications. Foundations and Trends in Theoretical Computer Science 1(2) (2005)Google Scholar
  9. 9.
    Saha, B.: Space Complexity of Estimating Aggregate Path Metrics over Massive Graph Streams and Related Metrics. Master’s thesis, IIT Kanpur, Computer Science (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sumit Ganguly
    • 1
  • Barna Saha
    • 1
  1. 1.Indian Institute of TechnologyKanpur

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