Weighted Universal Recovery, Practical Secrecy, and an Efficient Algorithm for Solving Both
In this paper, the authors consider a network of n nodes, each initially possessing a subset of packets. Each node is permitted to broadcast functions of its own packets and the messages it receives to all other nodes via an error-free channel. They provide an algorithm that efficiently solves the Weighted Universal Recovery Problem and the Secrecy Generation Problem for this network. In the Weighted Universal Recovery Problem, the goal is to design a sequence of transmissions that ultimately permits all nodes to recover all packets initially present in the network. They show how to compute a transmission scheme that is optimal in the sense that the weighted sum of the number of transmissions is minimized.