Dynamic routing and location services in metrics of low doubling dimension

We consider dynamic compact routing in metrics of low doubling dimension. Given a set of nodes V in a metric space with nodes joining, leaving and moving, we show how to maintain a set of links E that allows compact routing on the graph G(V, E). Given a constant ε ∈ (0, 1) and a dynamic node set V with normalized diameter Δ in a metric of doubling dimension α ∈ O(loglog Δ), we achieve a dynamic graph G(V, E) with maximum degree 2^O(α) log² Δ, and an optimal (9 + ε)-stretch compact name-independent routing scheme on G with (1/ε) ^O(α)log⁴ Δ-bit storage at each node. Moreover, the amortized number of messages for a node joining, leaving and moving is polylogarithmic in the normalized diameter Δ; and the cost (total distance traversed by all messages generated) of a node move operation is proportional to the distance the node has traveled times a polylog factor. (We can also show similar bounds for a (1 + ε)-stretch compact dynamic labeled routing scheme.) One important application of our scheme is that it also provides a node location scheme for mobile ad-hoc networks with the same characteristics as our name-independent scheme above, namely optimal (9 + ε) stretch for lookup, polylogarithmic storage overhead (and degree) at the nodes, and locality-sensitive node move/join/leave operations. We also show how to extend our dynamic compact routing scheme to address the more general problem of devising locality-sensitive Distributed Hash Tables (DHTs) in dynamic networks of low doubling dimension. Our proposed DHT scheme also has optimal (9 + ε) stretch, polylogarithmic storage overhead (and degree) at the nodes, locality-sensitive publish/unpublish and node move/join/leave operations.