Scale-free aggregation in sensor networks

We also propose a very simple randomized algorithm for routing information on a grid of sensors that satisfies the appropriate collision time condition. Thus, we prove that this simple scheme is a constant factor approximation (in expectation) to the optimum aggregation tree simultaneously for all correlation parameters k. The key contribution in our randomized analysis is to bound the average expected collision time of non-homogeneous random walks on the grid, i.e. the next hop probability depends on the current position.