On the Performance of Multi-Message Algebraic Gossip Algorithms in Dynamic Random Geometric Graphs

Abstract

In this letter, we investigate the performance of algebraic gossip algorithms for information dissemination in mobile ad hoc networks (MANETs). In the gossip algorithms, in each time slot, each node communicates with a neighboring node, which is randomly selected by an Exchange algorithm, to exchange their information. The goal of the algorithm is to efficiently disseminate all the messages to all the nodes as fast as possible. We analyze the convergence time of network coding (NC) based gossip algorithm by taking into account the node mobility in MANETs, and derived a lower bound on the convergence time. It showed that the convergence time of the NC gossip algorithm with node mobility can be reduced by the order of $O(n^{1/2}/\log ^{3/2}n)$ over that without considering node mobility. But it is only $O(\log n)$ quicker than the gossip algorithm with node mobility but no NC.