Gossip ("epidemic") algorithms can be used for computing aggregation functions of local values across a distributed system without the need to synchronize participating nodes. Although several (theoretical) studies have proven that these algorithms scale well with the number of nodes n, most of these studies are restricted to fully connected networks and based on rather strong assumptions, e. g., it is often assumed that all messages are sent at exactly the same time on different nodes. Applying gossip algorithms on non-fully connected networks significantly increases the number of messages / rounds, especially on weakly connected networks without a regular structure. We present new acceleration strategies for gossip-based averaging algorithms based on ant colony optimization, which specifically target weakly connected networks with irregular structure, where existing gossip averaging algorithms tend to be slow. The proposed acceleration strategies reduce the message and time complexity of standard gossip algorithms without any additional communication cost. The overhead only consists of additional local computation which is proportional to the node degree. All findings are confirmed experimentally for different types of network topologies and for different network sizes.

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