Counting arbitrary subgraphs in data streams

Authors:
Daniel M. Kane;Kurt Mehlhorn;Thomas Sauerwald;He Sun
Affiliations:
Department of Mathematics, Stanford University;Max Planck Institute for Informatics, Germany;Max Planck Institute for Informatics, Germany;Max Planck Institute for Informatics, Germany, Institute for Modern Mathematics and Physics, Fudan University, China
Venue:
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Year:
2012

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Abstract

We study the subgraph counting problem in data streams. We provide the first non-trivial estimator for approximately counting the number of occurrences of an arbitrary subgraph H of constant size in a (large) graph G. Our estimator works in the turnstile model, i.e., can handle both edge-insertions and edge-deletions, and is applicable in a distributed setting. Prior to this work, only for a few non-regular graphs estimators were known in case of edge-insertions, leaving the problem of counting general subgraphs in the turnstile model wide open. We further demonstrate the applicability of our estimator by analyzing its concentration for several graphs H and the case where G is a power law graph.