Optimal-stretch name-independent compact routing in doubling metrics

We consider the problem of name-independent routing in doubling metrics. A doubling metric is a metric space whose doubling dimension is a constant, where the doubling dimension of a metric space is the least value α such that any ball of radius <i>r</i> can be covered by at most 2^α balls of radius <i>r</i>/2.Given any δ>0 and a weighted undirected network <i>G</i> whose shortest path metric <i>d</i> is a doubling metric with doubling dimension α, we present a name-independent routing scheme for <i>G</i> with (9+δ)-stretch, (2+1<over>δ)^O(α) (log δ)² (log <i>n</i>)-bit routing information at each node, and packet headers of size <i>O</i>(log <i>n</i>), where δ is the ratio of the largest to the smallest shortest path distance in <i>G</i>.In addition, we prove that for any ε ∈ (0,8), there is a doubling metric network <i>G</i> with <i>n</i> nodes, doubling dimension α ≤ 6 - log ε, and Δ=<i>O</i>(2^1/ε<i>n</i>) such that any name-independent routing scheme on <i>G</i> with routing information at each node of size <i>o</i>(<i>n</i>^(ε/60)²)-bits has stretch larger than 9-ε. Therefore assuming that Δ is bounded by a polynomial on <i>n</i>, our algorithm basically achieves optimal stretch for name-independent routing in doubling metrics with packet header size and routing information at each node both bounded by a polylogarithmic function of <i>n</i>.