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  Deterministic Random Walks

Cooper, J., Doerr, B., Spencer, J., & Tardos, G. (2006). Deterministic Random Walks. In Proceedings of the Eighth Workshop on Algorithm Engineering and Experiments and the Third Workshop on Analytic Algorithmics and Combinatorics (ALENEX'06 / ANALCO'06) (pp. 185-197). Philadelphia, PA, USA: SIAM.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2281-9 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2282-7
Genre: Conference Paper

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 Creators:
Cooper, Joshua, Author
Doerr, Benjamin1, Author           
Spencer, Joel, Author
Tardos, Gábor, Author
Raman, Rajeev1, Editor           
Sedwgewick, Robert, Editor
Stallmann, Matthias F., Editor
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: Jim Propp’s P-machine, also known as ‘rotor router model’ is a simple deterministic process that simulates random walk on a graph. Instead of distributing chips to randomly chosen neighbors, it serves the neighbors in a fixed order. We investigate how well this process simulates a random walk. For the graph being the infinite path, we show that, independent of the starting configuration, at each time and on each vertex, the number of chips on this vertex deviates from the expected number of chips in the random walk model by at most a constant c1, which is approximately 2.29. For intervals of length L, this improves to a difference of O(log L) (instead of 2.29L), for the L2 average of a contiguous set of intervals even to O(√log L). It seems plausible that similar results hold for higher-dimensional grids Zd instead of the path Z.

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Language(s): eng - English
 Dates: 2007-04-262006
 Publication Status: Issued
 Pages: -
 Publishing info: Philadelphia, PA, USA : SIAM
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 314458
Other: Local-ID: C1256428004B93B8-DC59A2F138682FFAC1257299003BF463-DoerrANALCO06
 Degree: -

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Title: Untitled Event
Place of Event: Miami, FL, USA
Start-/End Date: 2007-03-09

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Title: Proceedings of the Eighth Workshop on Algorithm Engineering and Experiments and the Third Workshop on Analytic Algorithmics and Combinatorics (ALENEX'06 / ANALCO'06)
Source Genre: Proceedings
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Affiliations:
Publ. Info: Philadelphia, PA, USA : SIAM
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 185 - 197 Identifier: ISBN: 0898716101