Compact Oblivious Routing in Weighted Graphs

07/05/2020

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by   Philipp Czerner, et al.

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The space-requirement for routing-tables is an important characteristic of routing schemes. For the cost-measure of minimizing the total network load there exist a variety of results that show tradeoffs between stretch and required size for the routing tables. This paper designs compact routing schemes for the cost-measure congestion, where the goal is to minimize the maximum relative load of a link in the network (the relative load of a link is its traffic divided by its bandwidth). We show that for arbitrary undirected graphs we can obtain oblivious routing strategies with competitive ratio 𝒪̃(1) that have header length 𝒪̃(1), label size 𝒪̃(1), and require routing-tables of size 𝒪̃(deg(v)) at each vertex v in the graph. This improves a result of Räcke and Schmid who proved a similar result in unweighted graphs.