Paper Info
Title
Space-efficient Routing Tables for Almost All Networks and the Incompressibility Method
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
Year
DOI
Venue
1999
10.1137/S0097539796308485
SIAM J. Comput.
Keywords
DocType
Volume
upper bound,random graphs,space complexity,random graph,computer networks,network topology,lower bound,average case complexity,routing algorithms
Journal
28
Issue
ISSN
Citations 
4
0097-5397
10
PageRank 
References 
Authors
1.27
6
3
Name
Order
Citations
PageRank
Harry Buhrman11607117.99
Jaap-Henk Hoepman246053.96
Paul Vitányi32130287.76