Routing in distributed networks: overview and open problems
ACM SIGACT News
Compact and localized distributed data structures
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
On space-stretch trade-offs: lower bounds
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
Average stretch analysis of compact routing schemes
Discrete Applied Mathematics
An improved interval routing scheme for almost all networks based on dominating cliques
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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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