Distance estimation and object location via rings of neighbors
Aleksandrs Slivkins · 2005
We consider four problems on distance estimation and object location: low-stretch routing schemes [37], distance labeling [14], searchable small worlds [22], and triangulation-based distance estimation [24]. Focusing on metrics of low doubling dimension, we approach these problems with a common technique called rings of neighbors. Apart from improving the previously known bounds for these problems, our contributions include extending Kleinberg's small world model to doubling metrics, and a short proof of the main result in Chan et al. [9]. Doubling dimension is a combinatorial (non-geometric) notion of dimensionality that has recently become popular in the theoretical computer science literature.A collection of rings of neighbors is a sparse distributed data structure that captures the distance and routing information. The idea is that every node u stores pointers to some nodes called 'neighbors'; these pointers are partitioned into several 'rings', so that for some increasing sequence of balls Bi around u, the neighbors in the i-th ring lie inside Bi; the radii of these balls and the distribution of neighbors in a given ring depend on the specific application. In effect, rings of neighbors represent an overlay network with a certain structure imposed by the balls Bi. Although used implicitly in several contexts, rings of neighbors have not been articulated as a general proof technique.