The CPS 296.2 Geometric Optimization Class Project: Survey on Routing in Doubling Metric Space

Finding a shortest path between any two nodes in a network have been studied over the past few decades. A lot of routing algorithms for distributed networks have been introduced. In this paper, we consider routing in a doubling metric space. The doubling dimension is defined as the minimum value of α such that any radius-r ball can be covered by at most 2 radius-(r/2) balls. Doubling metric space is a metric space which doubling dimension is a constant. If α is O(log log n), a network has a low doubling dimension. Consider a large network graph G=(V, E). It is not practical to store all the information of other nodes in every node because of the limitation of space compacity. Therefore, a node must be able to deliver a packet to another node without knowing the whole picture of the graph. The effectiveness of a routing scheme is judged based on space compacity (storage per node) and stretch (the maximum ratio between the route and the shortest path among all n possible source-destination pairs).