Deterministic Random Walks on the Two-Dimensional Grid

  • Benjamin Doerr
  • Tobias Friedrich
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4288)


Deterministic and randomized balancing schemes are used to distribute workload evenly in networks. In this paper, we compare two very general ones: The random walk and the (deterministic) Propp machine. Roughly speaking, we show that on the two-dimensional grid, the Propp machine always has the same number of tokens on a node as does the random walk in expectation, apart from an additive error of less than eight. This constant is independent of the total number of tokens and the runtime of the two processes. However, we also show that it makes a difference whether the Propp machine serves the neighbors in a circular or non-circular order.


Random Walk Mathematical Intelligencer Unimodal Function Simple Random Walk Rotor Sequence 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Benjamin Doerr
    • 1
  • Tobias Friedrich
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

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