Private Information Retrieval on Multigraph-Based Replicated Storage

We consider the private information retrieval (PIR) problem for a multigraph-based replication system, where each set of $r$ files is stored on two of the servers according to an underlying $r$-multigraph. Our goal is to establish upper and lower bounds on the PIR capacity of the $r$-multigraph. Specifically, we first propose a construction for multigraph-based PIR systems that leverages the symmetry of the underlying graph-based PIR scheme, deriving a capacity lower bound for such multigraphs. Then, we establish a general upper bound using linear programming, expressed as a function of the underlying graph parameters. Our bounds are demonstrated to be tight for PIR systems on multipaths for even number of vertices.

Age of Gossip With Time-Varying Topologies

We consider a gossiping network, where a source node sends updates to a network of $n$ gossiping nodes. Meanwhile, the connectivity topology of the gossiping network changes over time, among a finite number of connectivity ''states,'' such as the fully connected graph, the ring graph, the grid graph, etc. The transition of the connectivity graph among the possible options is governed by a finite state continuous time Markov chain (CTMC). When the CTMC is in a particular state, the associated graph topology of the gossiping network is in the way indicated by that state. We evaluate the impact of time-varying graph topologies on the freshness of information for nodes in the network. We use the version age of information metric to quantify the freshness of information at the nodes. Using a method similar to the first passage percolation method, we show that, if one of the states of the CTMC is the fully connected graph and the transition rates of the CTMC are constant, then the version age of a typical node in the network scales logarithmically with the number of nodes, as in the case if the network was always fully connected. That is, there is no loss in the age scaling, even if the network topology deviates from full connectivity, in this setting. We perform numerical simulations and analyze more generally how having different topologies and different CTMC rates (that might depend on the number of nodes) affect the average version age scaling of a node in the gossiping network.

Age of Gossip with the Push-Pull Protocol

We consider a wireless network where a source generates packets and forwards them to a network containing $n$ nodes. The nodes in the network use the asynchronous push, pull or push-pull gossip communication protocols to maintain the most recent updates from the source. We use the version age of information metric to quantify the freshness of information in the network. Prior to this work, only the push gossiping protocol has been studied for age of information analysis. In this paper, we use the stochastic hybrid systems (SHS) framework to obtain recursive equations for the expected version age of sets of nodes in the time limit. We then show that the pull and push-pull protocols can achieve constant version age, while it is already known that the push protocol can only achieve logarithmic version age. We then show that the push-pull protocol performs better than the push and the pull protocol. Finally, we carry out numerical simulations to evaluate these results.