Space-efficient routing tables for almost all networks and the incompressibility method

Harry Buhrman, Jaap-Henk Hoepman, Paul Vitanyi

    Research output: Contribution to journalArticleAcademicpeer-review

    9 Citations (Scopus)
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    Abstract

    We use the incompressibility method based on Kolmogorov complexity to determine the total number of bits of routing information for almost all network topologies. In most models for routing, for almost all labeled graphs, $\Theta (n^2)$ bits are necessary and sufficient for shortest path routing. By "almost all graphs" we mean the Kolmogorov random graphs which constitute a fraction of 1 - 1/nc of all graphs on n nodes, where c > 0 is an arbitrary fixed constant. There is a model for which the average case lower bound rises to $\Omega(n^2 \log n )$ and another model where the average case upper bound drops to $O(n \log^2 n)$. This clearly exposes the sensitivity of such bounds to the model under consideration. If paths have to be short, but need not be shortest (if the stretch factor may be larger than 1), then much less space is needed on average, even in the more demanding models. Full-information routing requires $\Theta (n^3)$ bits on average. For worst-case static networks we prove an $\Omega(n^2 \log n )$ lower bound for shortest path routing and all stretch factors < 2 in some networks where free relabeling is not allowed.
    Original languageEnglish
    Pages (from-to)1414-1432
    JournalSIAM journal on scientific computing
    Volume28
    Issue number4
    DOIs
    Publication statusPublished - 1999

    Keywords

    • Computer networks
    • Routing algorithms
    • Compact routing tables
    • Kolmogorov complexity
    • Incompressible method
    • Random graphs
    • Average-case complexity
    • Space complexity

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