Computing strongly connected components in the streaming model

  • Authors:
  • Luigi Laura;Federico Santaroni

  • Affiliations:
  • Dep. of Computer Science and Systems, Sapienza Univ. Of Rome, Roma;Dep. of Computer Science, Systems and Production. Univ. of Rome "Tor Vergata", Roma

  • Venue:
  • TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
  • Year:
  • 2011

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Abstract

In this paper we present the first algorithm to compute the Strongly Connected Components of a graph in the datastream model (W-Stream), where the graph is represented by a stream of edges and we are allowed to produce intermediate output streams. The algorithm is simple, effective, and can be implemented with few lines of code: it looks at each edge in the stream, and selects the appropriate action with respect to a tree T, representing the graph connectivity seen so far. We analyze the theoretical properties of the algorithm: correctness, memory occupation (O(n log n)), per item processing time (bounded by the current height of T), and number of passes (bounded by the maximal height of T). We conclude by presenting a brief experimental evaluation of the algorithm against massive synthetic and real graphs that confirms its effectiveness: with graphs with up to 100M nodes and 4G edges, only few passes are needed, and millions of edges per second are processed.