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Monitoring of Domain-Related Problems in Distributed Data Streams

  • Pascal Bemmann
  • Felix Biermeier
  • Jan Bürmann
  • Arne Kemper
  • Till Knollmann
  • Steffen Knorr
  • Nils Kothe
  • Alexander Mäcker
  • Manuel MalatyaliEmail author
  • Friedhelm Meyer auf der Heide
  • Sören Riechers
  • Johannes Schaefer
  • Jannik Sundermeier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10641)

Abstract

Consider a network in which n distributed nodes are connected to a single server. Each node continuously observes a data stream consisting of one value per discrete time step. The server has to continuously monitor a given parameter defined over all information available at the distributed nodes. That is, in any time step t, it has to compute an output based on all values currently observed across all streams. To do so, nodes can send messages to the server and the server can broadcast messages to the nodes. The objective is the minimisation of communication while allowing the server to compute the desired output.

We consider monitoring problems related to the domain \(D_t\) defined to be the set of values observed by at least one node at time t. We provide randomised algorithms for monitoring \(D_t\), (approximations of) the size \(|D_t|\) and the frequencies of all members of \(D_t\). Besides worst-case bounds, we also obtain improved results when inputs are parameterised according to the similarity of observations between consecutive time steps. This parameterisation allows to exclude inputs with rapid and heavy changes, which usually lead to the worst-case bounds but might be rather artificial in certain scenarios.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Pascal Bemmann
    • 1
  • Felix Biermeier
    • 1
  • Jan Bürmann
    • 1
  • Arne Kemper
    • 1
  • Till Knollmann
    • 1
  • Steffen Knorr
    • 1
  • Nils Kothe
    • 1
  • Alexander Mäcker
    • 1
  • Manuel Malatyali
    • 1
    Email author
  • Friedhelm Meyer auf der Heide
    • 1
  • Sören Riechers
    • 1
  • Johannes Schaefer
    • 1
  • Jannik Sundermeier
    • 1
  1. 1.Computer Science Department, Heinz Nixdorf InstitutePaderborn UniversityPaderbornGermany

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