Network Connectivity--Information Freshness Tradeoff in Information Dissemination Over Networks

TL;DR

This work studies the timeliness of information diffusion in gossip networks through the version age metric, bridging the gap between highly connected and sparsely connected topologies. It introduces tightened recursive bounds on the age of a connected set and applies them to structured graphs—2D grids, generalized rings, and hypercubes—revealing how network geometry governs information freshness. The results uncover a connectivity-information freshness tradeoff, deriving explicit scaling laws (e.g., $v_1=O(n^{1/2})$ vs $O(n^{1/3})$ for grids, and $O(\log n)$ for hypercubes under certain regimes) and providing numerical validation across topologies. The findings offer design guidance for decentralized networks, indicating how choosing topology and connectivity levels impacts the timeliness of updates in time-critical applications.

Abstract

We consider a gossip network consisting of a source generating updates and $n$ nodes connected according to a given graph structure. The source keeps updates of a process, that might be generated or observed, and shares them with the gossiping network. The nodes in the network communicate with their neighbors and disseminate these version updates using a push-style gossip strategy. We use the version age metric to quantify the timeliness of information at the nodes. We first find an upper bound for the average version age for a set of nodes in a general network. Using this, we find the average version age scaling of a node in several network graph structures, such as two-dimensional grids, generalized rings and hyper-cubes. Prior to our work, it was known that when $n$ nodes are connected on a ring the version age scales as $O(n^{\frac{1}{2}})$, and when they are connected on a fully-connected graph the version age scales as $O(\log n)$. Ours is the first work to show an age scaling result for a connectivity structure other than the ring and the fully-connected network, which constitute the two extremes of network connectivity. Our work helps fill the gap between these two extremes by analyzing a large variety of graphs with intermediate connectivity, thus providing insight into the relationship between the connectivity structure of the network and the version age, and uncovering a network connectivity--information freshness tradeoff.

Figures (16)

• Figure 1: A gossip network where the node in light yellow is the source generating updates and sending them to a network of nodes connected in a two-dimensional grid. There are no boundaries in the grid, and all nodes have four neighbors.
• Figure 2: A gossip network where the gossiping nodes form a generalized ring network. The source node updates itself at rate $\lambda_e$, and disseminates information to nodes arranged in a ring at rate $\lambda$. Each node communicates with $f(n)$ nodes on each of its side, thus communicating with $2f(n)$ nodes in total.
• Figure 3: The evolution of a unit hypercube network, from one dimension to four dimensions.
• Figure 4: A three-dimensional hypercube network with side length five.
• Figure 5: All nodes have four connections. Nodes that are seemingly at the boundary in Fig. \ref{['fig_grid_network']} are connected in a wrap-around fashion to the nodes on the opposite side of the row or column.

Theorems & Definitions (23)

• Lemma 1
• Lemma 2
• Lemma 3
• Theorem 1
• Remark 1
• Lemma 4
• Lemma 5
• Theorem 2
• Remark 2
• Lemma 6