Compact Oblivious Routing in Weighted Graphs

TL;DR

This paper introduces compact oblivious routing schemes for weighted graphs that achieve low congestion with small routing tables, header length, and label size, improving upon previous unweighted graph results.

Contribution

It presents the first oblivious routing strategies for weighted graphs with competitive ratio $ ilde{O}(1)$ and small routing tables, header, and label sizes.

Findings

Achieves $ ilde{O}(1)$ competitive ratio for congestion in weighted graphs.

Routing tables require only $ ilde{O}( ext{deg}(v))$ space per vertex.

Improves upon previous results limited to unweighted graphs.

Abstract

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 $\tilde{\mathcal{O}}(1)$ that have header length $\tilde{\mathcal{O}}(1)$, label size $\tilde{\mathcal{O}}(1)$, and require routing-tables of size $\tilde{\mathcal{O}}(\operatorname{deg}(v))$ at each vertex $v$ in the graph. This improves a result of R\"acke and Schmid who proved a similar result in unweighted graphs.