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On Estimating Path Aggregates over Streaming Graphs

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

Abstract

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.

Keywords

Data Stream Connected Graph Transitive Closure Simple Path Adjacency List 
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.

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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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