On a New Competitive Measure for Oblivious Routing

Oblivious routing algorithms use only locally avail¬able information at network nodes to forward traffic, and as such, a plausible choice for distributed implementations. It is a natural desire to quantify the performance penalty we pay for this distributedness. Recently, Racke has shown that for general undirected graphs the competitive ratio is only O(log n), that is, the maximum congestion caused by the oblivious algorithm is within a logarithmic factor of the best possible congestion. And while the performance penalty is larger for directed networks (Azar gives a O(vn) lower bound), experiments on many real-world topologies show that it usually remains under 2. These competitive measures, however, are of worst-case type, and therefore do not always give adequate characterization. The more different combinations of demands a routing algorithm can accommodate in the network without congestion, the better. Driven by this observation, in this paper we introduce a new competitive measure, the volumetric competitive ratio, as the measure of all admissible demands compared to the measure of demands routed without congestion. The main result of the paper is a general lower bound on the volumetric ratio; and we also show a directed graph with O(1) competitive ratio that exhibits O(n) volumetric ratio. Our numerical evaluations show that the competitivity of oblivious routing in terms of the new measure quickly vanishes even in relatively small common-place topologies.